We don't have many mentions of it from the Middle Ages, but they were certainly interested. Human remains have been found from the Saxon era, particularly a man who was decapitated around the age of 30, which suggests that the site was used as an execution grounds. There is, however, no mention of Stonehenge in early medieval sources. Although the limited evidence means we can't say with certainty when interest in the sight took off in the Middle Ages, it seems to have been the twelfth century at the latest. By the 1120s, the historian Henry of Huntingdon felt confident in describing it as one of the four wonders of England:

There are four wonders which may be seen in England […] The second is at Stonehenge, where stones of remarkable size are raised up like gates, in such a way that gates seem to be placed on top of gates. And no one can work out how the stones were so skilfully lifted up to such a height or why they were erected there.

At this stage, there doesn't seem to have been much interest in the site beyond "huh, that's neat, I wonder how that was built." However, because of its strangeness it eventually found itself a part of English mythology. At the same time Henry was writing, another man named Geoffrey of Monmouth was busy filling the gaps in the history of early medieval England with stories he wove together from fragments of earlier dodgy histories and his own imagination. It is from Geoffrey of Monmouth that we get the legend of King Arthur, and he couldn't pass up the chance to weave a mysterious place like Stonehenge into his narrative. Because nobody knew how Stonehenge was built, Geoffrey went with the obvious explanation of "Whenever you notice something like that, a wizard did it." According to Geoffrey's narrative - which was treated as authoritative in the Middle Ages - Stonehenge was created as a war memorial. Geoffrey features a guy called Aurelius Ambrosius. He was a real guy (though his names were the other way around), but Geoffrey reinvented him as a mythical British king. His narrative is quite long, but here are the important bits:

As Aurelius looked upon the place where the dead lay buried, he was moved to great pity and burst out in tears. For a long time he considered many different ideas about how to memorialise this site, for he felt that some kind of monument should grace the soil that covered so many noblemen who had died for their homeland...

Merlin said to him: “If you wish to honour the grave of the men with something that will last forever, send for the Ring of Giants which is in now atop Mount Killaraus in Ireland. This Ring consists of a formation of stones that no man in this age could erect unless he employed great skill and ingenuity. The stones are enormous, and there is no one with strength enough to move them...

"These stones are magical and possess certain healing powers. The giants brought them long ago from the confines of Africa and set them up in Ireland when they settled that country. They set the Ring up thus in order to be healed of their sickness by bathing amid the stones, for they would wash the stones and then bathe in the water that spilled from them; they were thus cured of their illness. They would even mix herbs in and heal their wounds in that way. There is not a stone among them which does not have some kind of medicinal power.” When the Britons heard Merlin’s words, they agreed to send for the stones and to attack the people of Ireland if they tried to withhold them...

Having achieved this victory, the Britons went up Mount Killaraus and gazed at the ring of stones in gladness and wonder. As they all stood there, Merlin came among them and said: “Use all of your strength, men, and you will soon discover that it is not by sinew but by knowledge that these stones shall be moved.” They then agreed to give in to Merlin’s counsel and, through the use of many clever devices, they attempted to dismantle the Ring...

Seeing all of their efforts fall flat, Merlin laughed and then rearranged all of their devices. When he had arranged everything carefully, the stones were removed more easily than can be believed. Merlin then had the stones carried away and loaded onto the ships...

The stones were set up in a circle around the graves exactly as they had been arranged on Mount Killaraus in Ireland. Merlin thus proved that his craft was indeed better than mere strength.

That became the authoritative account of what Stonehenge was and how it was built. The fourteenth century chronicle Scala Mundi notes during the reign of Aurelius Ambrosius:

That year the Giants’ Carol of Ireland, not by force but by the art of Merlin, was conveyed to Stonehenge.

If you asked someone in the Middle Ages from the later thirteenth century onwards what Stonehenge was, it is likely that they would say it was a war memorial built through the cleverness of Merlin to commemorate British lords killed by the Saxons, and that this war memorial was essentially a translation of a magic circle in Ireland built by African giants. This took it from the neat thing Henry of Huntingdon wrote about to a part of England's construction of its own mythology.