The Bosnian spend the second half of last season on loan on Teesside and had been expected to make that move permanent in the summer, only for a deal to fall through on deadline day over "excessive agent demands".
However, it appears that the 25-year-old will get his move after the two clubs agreed a deal in principle for the German-born star to move to the Riverside on a season-long loan.
At this moment in time it is unclear whether the move includes an option to buy.
Besic traveled to Boro's Rockliffe Park training ground on Sunday for talks and is believed to have agreed to return to his former stomping ground to aid the club's pormotion push.
His arrival will further strengthen the club's options in midfield, with Adam Clayon, Jonny Howson, Paddy McNair, Grant Leadbitter, Lewis Wing and Julien de Sart all currently on the books at the club.
Besic could be joined at Boro by Everton team-mate Yannick Bolasie, who was on Teesside for talks with Tony Pulis on Monday.