Toney is currently serving a ban for gambling breaches, but returned to training last month with Brentford.
He is scheduled to return to the pitch in January after serving his eight-month ban but there are suggestions that could move on in the winter window.
The forward will have 18 months left on his Brentford contract in January and Arsenal and Chelsea are amongst the clubs who are interested in signing him.
But it has been claimed that Brentford are yet to be approached by any club ahead of the January window.
Brentford boss Thomas Frank is hopeful that the forward will stay at the club once he returns from the ban.
However, the club have not ruled out selling the player if they receive the right offer for the striker.
But it has been claimed that it would take a big offer to prize him out of Brentford in the middle of the season.
Toney will be keen to hit the ground running once he returns in order to be in Gareth Southgate’s England plans for next summer’s European Championship.