Abraham has scored 16 goals for Villa this season and Wolves head coach Nuno Espirito Santo has identified him as a priority signing to sharpen up his squad's attack.
Having made his first-team debut for the Blues back in May 2016, Abraham spent the next season away on loan at Bristol City and enjoyed vast success but failed to reach those heights with Swansea City in 2017-18.
Wolves have had an £18milllion bid accepted by Chelsea for striker Tammy Abraham.
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A host of top European clubs in Bayern Munich, Paris Saint-Germain and Juventus are keeping tabs on the dynamic Welsh midfielder. The Switzerland worldwide scored the opening goal as the Gunners sealed a 4-1 win at the Emirates Stadium.
The Blues will want their talented 21-year-old playing regular football, but if this was on offer in the top flight it could put Villa's current deal in jeopardy.
He's on loan for the season from Chelsea but can be recalled and then loaned out again in January. He is very happy and you can see the connection he has the supporters, the players and staff. For all three parties it is a win, win, win.
Under Fifa rules, no player can play in official matches for more than two teams in one season but it is not thought Abraham's substitute appearance for Chelsea in this season's Community Shield will prevent him making the move as it is not regarded as an "official game". But it is not in my control.
No fee has been agreed with Chelsea for the striker's services.