The 21-year-old spent the 2018-19 campaign on loan at Villa Park and his 26 goals helped to secure promotion to the Premier League through the Championship play-offs.
Dean Smith would welcome the England Under-21 international back into his plans for a return to the top tier, but Abraham is determined to make his mark at Stamford Bridge.
Staying put would be his preference, but the door is not being closed on a return to the West Midlands as he seeks to find the regular football his ongoing development requires.
Abraham told Sky Sports: "You can never say never.
"Chelsea is obviously the club that I have been at since a young [boy] so the aim is to try and breakthrough there.
"Like I say, you can never say never. We'll see how things look."
Abraham has kept an eye on the 2019-20 schedule for both of the sides he has had strong ties to of late.
"I looked at both, I was excited," said Abraham.
"It's good to see Aston Villa in the Premier League so I still follow them on social media - I always look out for them as well."
For now, Abraham’s focus is locked on the European U21 Championship in Italy and San Marino.
With two senior caps to his name, a proven performer will be expected to lead the charge for Aidy Boothroyd’s side.
Once his involvement in that competition has come to a close, Abraham will be freed to make a decision on his future.
As things stand, he has taken in just three competitive outings for Chelsea, with the vast majority of his senior experience at club level having been picked up during loans at Bristol City, Swansea and Villa.