Burey was a bit part player at Millwall last season and scored just once in 24 Championship appearances for the club.
The Lions have been keen to listen to offers for him and he has been attracting interest from clubs in League One.
But it has been claimed that he is close to agreeing to join Oxford United in the ongoing transfer window.
A deal is in place between the two clubs for a loan deal and Oxford have permission from Millwall to hold talks with Burey.
The League One club are confident of convincing the player to accept a move to the Kassam Stadium this summer.
Oxford had previously tabled a bid for the striker but he was not keen to permanently drop down to League One.
But he is more receptive to a loan move and Oxford are confident of securing his signature soon.
