Short answer:

During the late medieval and early Renaissance academic travel was surprisingly common. Students weren't aiming for anything like the 120-130 credit hours to graduate that you might see today. In this era many students neither sat examinations nor attained any degree, most were more like auditors today. In the 15th century, one begins to see university education that resembles current practices of study.

Discussion:

Students often traveled to pursue their academic interests, but there were no credits to transfer in the sense of a contemporary American university. European universities of this time typically had little coursework: you attended lectures, and after a number of years you might or might not pass your examinations or be awarded a degree. A degree oriented course of study was unusual, and the terms would be quite specific. Latin was the language of instruction everywhere, and the examinations were substantially the same until the 17th century. Many students never took them, content to just . . . be a student

From the perspective of today, the great proportion of medieval university attenders would have to be classified as drop-outs or even failures. As late as 1500, it was by no means normal to sit any form of examination. The vast majority were satisfied to attend and belong. The social possibilities opened up by the university did not yet require control by a special system of entitlement based on examinations and graduation.

What was important was your relationship with the institution itself, and at least some places and times it was not only easy to change schools, it was the norm. In Germany, for example, Alan Ross tells us that 17th century German pupils changed schools quite often-- it was a lengthy educational career, and it was common for students to have to move several times during their studies.

There was substantial academic tourism-- students with particular interests did go to centers of knowledge to learn what they couldn't at home, or just to get away from home. There's even a specific term for it, the peregrinatio academica (= "academic pilgrimage"). Northern Italy was celebrated for law and medicine, and English students frequently attended universities in Bologna and Padua.

Hilde De Ridder-Symoens has found this wonderful description by Jacques de Vitry of the various nationalities studying in Paris and making the Latin Quarter the party town of the age

"The English are drunken cowards, the French proud, soft and effeminate; the Germans are quarrelsome and foul-mouthed, the Normans vain and haughty, the men of Poitou treacherous and miserly, the Burgundians stupid brutes, the Bretons frivolous and flighty, the Lombards miserly, spiteful and evil-minded, the Romans vicious and violent, the Sicilians tyrannical and cruel, the men of Brabant are thieves and the Flemings are debauched"

Continental universities typically had separate "colleges" housing young men of the various nations studying there; these date to the Middle Ages. Later, the "Grand Tour" for wealthy young gentlemen became the Junior Year abroad of the early modern era, and a healthy source of cash for the destinations. If you had the cash, a foreign university was happy to take it.

But in a contrary tendency, at certain places and times we see a rise in academic parochialism:

When the emperor Frederick II founded the Naples studium in 1224, to ensure its survival he forbade his subjects to frequent any other studium. Similar protective measures were taken to benefit the University of Pavia in 1361, 1392, and 1412, and the University of Padua in 1407 and 1468.

So any definitive answer to your question really requires a specifying "which student, studying with whom, moving between which colleges at which universities, when-- precisely". Matriculation, the entry into a university community, was a formal and documented procedure, with legal and financial rights and obligations that substantially exceed the distinction between a Dartmouth student and an Amherst student today. So "could you transfer" is a bit like asking "could a Cistercian become a Dominican". You weren't so much transferring credit hours as joining a new community.

You will find a distinction made between veri scholares and falsi scholares -- essentially "true students" and "false" ones. Universities and their administrations were often quite willing to affiliate random "students" for a payment-- but whether that young was a bona fide matriculated student eligible for a degree was often more than a little ambiguous.

In the course of the fifteenth century, it came to be less a matter of excluding the falsi scholares than of enforcing a universal registration. Anybody who disregarded this or even flouted it was in some places considered almost a rebel. Finally, it was with the aid of the universal matriculation registers that the university was able to control its 'most sacred duty', which was the award of academic degrees, of doctorates, along with the grant of the licentia docendi to those who were regarded suitable for it.

Yet supervision by masters or administration by rectors did not necessarily work smoothly or even completely. It was not unusual for doctors and masters first and foremost to be entrepreneurs, especially if they taught in private houses or colleges and halls. Many made their livelihood exclusively from the fees of paying guests and 'auditors'. Here and there, they satisfied to their own advantage the demand for 'private' affiliation to a university. Many of those attending the university were able to enjoy exemptions from judicial proceedings and taxes while there. They were even able to study and to graduate 'unofficially', without complying with the legal and financial claims of the university as a whole.

Sources:

Woolfson, Jonathan. “Padua and English Students Revisited.” Renaissance Studies, vol. 27, no. 4, 2013, pp. 572–587.

Rainer Christoph Schwinges, "Admission" in Hilde De Ridder-Symoens (ed.), A History of the University in Europe, (Cambridge:1996)

ROSS, ALAN S. “PUPILS' CHOICES AND SOCIAL MOBILITY AFTER THE THIRTY YEARS WAR: A QUANTITATIVE STUDY.” The Historical Journal, vol. 57, no. 2, 2014, pp. 311–341.,