Abraham, who joined Villa on a season-long loan deal from Chelsea the summer transfer window, has been linked with moves away from the Villa in the January transfer window.
According to The Birmingham Mail, Palace are interested in signing the striker on loan from Chelsea for the second half of the season.
The Express & Star has reported that Wolves are still interested in the England international despite the 21-year-old turning their initial offer down.
Villa manager Smith has said that Abraham has been training with a smile on his face ahead of the Championship match against Wigan Athletic away from home on Saturday afternoon.
Smith told The Birmingham Mail about Abraham: “He’s training, training well and with a smile on his face.
“He’s been scoring goals in training and is enjoying his football at Aston Villa, pretty much what I said before.”
Encouraging for Aston Villa fans
Abraham seems focused on Villa at the moment, and that will be very encouraging for the Villa Park faithful.
The Villans need the striker to score the goals as regularly as he has done so far this season, as Smith’s side continue their quest for the Championship playoffs.