A lot of people have pointed out that the activities involved with the Islamic Meccan pilgrimage today seem to be an attempt to copy the experience of a pilgrimage to either Jerusalem (by Jews or Christians) or to Petra (by pagans).
At the Hypotyposeis blog, there are two posts about something that St. Clement of Alexandria (in his book Stromateis) says was a Jewish custom: they would make seven circuits around the Temple before entering it. (And this would be similar to what the Israelites did while waiting for the walls of Jericho to fall, in the Book of Joshua.)
In one post, the Hypotyposeis blog relates this passage in Clement to an ambiguous Greek word, periboloun, which can mean either “going around a circuit” or “a covering wrapping around something.”
This would obviously be a more understandable reading, because seven different materials that acted as “coverings” or “veils” were used for the Temple’s Tabernacle.
His latest post relates the circuit idea itself to a passage in the Jewish historian Josephus, which talks about the “seven purities” observed in the process of approaching the Tabernacle. This is the idea of increasing levels of purity being required of those entering further and further into the courts of the Temple.
Either way, it seems clear that there was an idea floating around the Middle East that Jews circled around the Temple or the Tabernacle. Since ritual circuits were common in paganism and at Christian pilgrimage sites and shrines, it would be pretty normal to try to transfer a Jerusalem custom to the Kaaba, in order to make some kind of point to Jewish people. (Whether or not it would be understood as intended.)