The 32-year-old United States midfielder is set to join Slaven Bilic's side until the end of the season after being allowed to leave the Bundesliga club.
Jones' contract expires at the end of the season, so his long spell at the Gelsenkirchen outfit appears to be over.
Besiktas posted a picture of Jones undergoing a medical on their official website on Thursday.
Jones joined Schalke from Eintracht Frankfurt back in 2007 and has made well over 100 appearances for the club, including 14 in the Bundesliga this season and five in the UEFA Champions League.
He spent a loan spell with Blackburn Rovers in 2011 and also played for Bayer Leverkusen earlier in his career.
Istanbul club Besiktas are fourth in the Super Lig table, 14 points behind leaders Fenerbahce.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
