The France international has emerged as a target for Unai Emery, who is also keen to recruit Nicolas Jackson from the west London club before the September 1 deadline.
Villa have so far been unable to match the terms of the loan fee Chelsea want for Jackson and are hoping those demands will reduce over the coming days.
Nkunku, who like Jackson has been told he can leave Stamford Bridge this summer, has emerged as a possible alternative.
The 27-year-old has struggled for consistency since arriving in the Premier League from RB Leipzig two summers ago, starting just nine top flight matches last season.
Emery is eager to freshen up his forward line with Villa having failed to score in either of their opening two matches.
Evann Guessand, who joined from Nice earlier this month for an initial £23.5million fee, has been their only “big money” addition.
Emery hinted after Saturday’s 1-0 defeat at Brentford how the uncertainty surrounding many of his players had hindered preparations for the campaign.
Villa have moved more than a dozen senior players off the books but the manager suggested more could still follow.
He said: “We have to clarify some things in the transfer window in the next week.
“We have enough players but we need to clarify some circumstances with some players, whether they are staying or not, and the possibility of adding someone to help us.”