The Teesiders remain keen on adding to their squad, with boss Tony Pulis keen to reunite with Puncheon, having previously worked with him during his time in charge at Selhurst Park.
Palace are thought to have told Puncheon he is free to leave the club on loan, with the experienced midfielder some way down the pecking order under Roy Hodgson.
“He wants to play more and I have made it clear to him I cannot guarantee that. In the middle of the park is where we are, at the moment, very competitive. But you saw that he is still a very good player, and I thought he was important to us in our victory," Hodgson admitted following the narrow 1-0 victory over Swansea in the Carabao Cup on Tuesday night.
A set-piece specialist able to play in a variety of positions, Puncheon could be a shrewd addition to Pulis' side, particularly with Boro forward Martin Braithwaite pushing for a move away from the club.