The Mirror says Wolves have made the England striker a prime January target and are keen on taking the 21-year-old from Stamford Bridge in a potential £18million deal.
Abraham has starred for Aston Villa on loan in the Championship this season, scoring 16 goals in 20 games.
Wolves officials have been working to ascertain whether Abraham would be eligible to play for the club this season, having already featured for both Villa and Chelsea. He also featured in a Premier League 2 match against Derby County, leading to questions over his eligibility.
But Wolves can cite precedent, such as Liam Walsh, who played for Birmingham City, Bristol City and Everton's U-23 side last season, but whose switch to the Robins was allowed by the FA - without help from FIFA.