Marcelo Bielsa is reportedly aiming the sign the Bosnian midfielder on a permanent deal before the transfer window shuts at 5 pm on Thursday.
The report claims that Leeds are planning to submit a bid in the region of £4.5million for the 25-year-old defensive midfielder.
Besic joined Everton in 2014 but his career never really kicked on at the Merseyside club, with the player suffering a cruciate ligament injury on his right knee during the 2016-17 season.