Albanian is a separate branch on the Indo-European language tree, somewhat removed from both Latin and Greek and is one of the oldest living languages today. There's significant debate over where proto-albanian (Albanian's ancestor) comes from, and there's arguments for all sides. Some believe that Albanian derives from ancient Illyrian, which was a language that dominated the eastern adriatic sea. However, this theory is kind of iffy, and mainly holds traction among Albanian sympatheziers to give the Albanian people a more ancient hold on the region.

Others, like Vladimir Orel, believe that Albanian came from elsewhere. In his book "Albanian Etymological Dictionary", Vladimir Orel basically summarizes the current view of Albanian origin, which denotes that the language did not arise on the coast but, in fact, away from it. Orel states that the language arose from populations along the southern Carpathian mountains due to several reasons. First, the lack of Albanian words to describe Illyrian toponomy, with the populations instead using borrowed Latin, Hellenic, or other terms for the local landmarks and regions. Second, the lack of Albanian words to describe things having to do with the sea or coast. A large portion of Albanian words with objects having to do with the sea (shark, boat, sea, etc.) are borrowed from either Latin or Greek. Next, some toponomy in the region that Orel hypothesizes Albanians originated from (the southern Carpathians) have certain landmarks which seem to be derived from proto-albanian, and not the other languages.

Linguistically, there is strong evidence to suggest that the Albanian speaking population did not arise on the coastlines of the Adriatic and the Ionian (where they are present now, which used to be under ancient illyria) and instead arose from a different region. Additionally, it is not related to Latin or Greek except through Indo-European. However, throughout history there has been significant linguistic "trading" (for lack of a better word) between the settled Albanian populations and its surrounding areas, simply due to the fact that the modern-day Albanian region has almost always been under the control of foreign powers.

Under Orel's hypothesis, the Albanian-speaking populations which settled in modern-day Albania settled prior to the Roman conquest of it. This means that almost immediately the Albanian populations were put under foreign control, and would remain so. From the Latin-speaking Roman Empire, the land was then more or less transferred to the Greek/Latin Eastern Roman Empire, then to the Bulgars and the Serbs before being able to form their own independent kingdoms until the rise of the Ottomans, where they were subjugated under the Ottomans for the next ~500 years.

So, while Albanian is not all that related to Latin or Greek, it has been heavily influenced by both (and more recently by Turkish) so much so that I, a native Albanian speaker, sometimes have trouble finding words which aren't foreign loan words. While the grammar has remained Albanian, many of the words have not. There has been significant contact between the modern Albanian region & its historical populations with its conquerors like the Roman Empire, the Eastern Roman Empire, the Serbian Empire, and the Ottoman/Turkish Empire, and their influences on Albanian survive to this day.

What is your source on it not having ties to either? The two major dialects are Greek influenced Albanian and Latin Influenced Albanian.