Middlesbrough boss Neil Warnock is keen on a reunion with Bolasie, who played under him at Crystal Palace, but time is short in the domestic transfer window.
And for the deal to happen, Everton would need to agree to pick up the tab for a large chunk of the winger’s salary.
Bolasie is out of favour at Goodison Park, but it remains to be seen how much of his wages the Toffees would be prepared to pay in order to shift him out before Friday evening’s deadline
The winger is claimed to be keen on making the move to Middlesbrough.
He came close to joining Middlesbrough two years ago, but chose instead to head to Villa Park and Aston Villa.
Bolasie spent last term on loan in Portugal at Sporting Lisbon.
The 31-year-old has made just 32 appearances for Everton since joining the club in 2016 and is into the final year of his deal at Goodison Park.