The main basis of the claim is that the physical objects described in the holy books are clearly apparent in the alternative site instead of in the Sinai Peninsula[2]. The secondary basis is the fact (mentioned in both Old Testament and Quran) that Jethro (Arabic Shuaib) is believed to be the father-in-law of Moses when he went into hiding for many years in Midian (northwest Saudi Arabia) and got married there[3]. Fun facts, most of the 25 prophets well-known in Islam are of Jewish origin including Moses and Jesus, and Jethro/Shuaib and Muhammad are a few handful of Arabic prophets [4].
Also a little known fact is that city of Mecca in Saudi is referenced in both the Old Testament and Quran as Baka and Bakkah Valley, respectively [5]. In the 7th century Arabic it was common practice to interchange letter M and B.
[1]http://etheses.dur.ac.uk/3224/1/1.pdf
[2]https://www.youtube.com/watch?v=YjrxHqNy5CQ
[3]https://en.wikipedia.org/wiki/Midian
[4]https://en.wikipedia.org/wiki/Prophets_and_messengers_in_Isl...