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.
Former Villa star Dublin has suggested what Abraham lacks to play for Chelsea in the Premier League at the moment.
Football.London quotes Dublin as saying about Abraham: "The only thing that Tammy's missing, for me as a former centre-forward, is that little bit of a horrible edge that you need.
"Talent-wise, he's got everything. I just think he needs to be a little bit more horrible to get the big numbers in the big league."
Abraham did not have a good time for Swansea City in the Premier League last season, as the 21-year-old striker was able to scored just five goals in 1721 minutes of league football for the Swans, according to WhoScored.