Turkish outlet Ajansspor reports that Galatasaray were willing to accept offers of £7.9m for Falcao, however due to the financial power of both interested clubs, the Istanbul giants are now holding out for a transfer fee of around £15.9m.
Barcelona legend and current Al-Sadd manager Xavi Hernandez is interested in bringing the former La Liga rival to the Qatari club with an offer of £11.4m understood to be on the table for the striker's services.
Saudi Arabian club Al-Hilal have also made an offer and the Colombian has reportedly already met with their representatives.
Falcao's contract runs out in June 2022, however he could be on the move before then.
The 34-year-old has made 89 international appearances and has scored over 200 goals in a club career playing in some of Europe's biggest leagues for the likes of Porto, Atletico Madrid, Chelsea and Manchester United.