The report adds that Burnley and Huddersfield are also interested in signing him.
The 21-year-old is currently on loan at Aston Villa, where he has scored 14 goals this season. However, his loan spell is in danger of being cut short with several Premier League clubs vying for his signature.
Chelsea are looking to recall their striker in January, and this could open the window of opportunity for other clubs to sign him. Abraham has proved himself in the Championship, but a potential move to the Premier League could be tempting for him.
Both Wolves and Crystal Palace are looking to sign a natural finisher in January to bolster their attacking department, and Abraham would be a superb addition for them.
Although Abraham did struggle during his spell at Swansea City when they were in the Premier League, he is young and has the potential to score regularly at this level.