Nkunku was on Villa’s list of targets heading into the final weeks of the transfer window and they had enquired about taking the France international on loan.
But he is now due to undergo a medical in Italy on Thursday night, after agreeing a permanent exit from the London club.
Villa are also facing an uphill struggle in efforts to sign another Chelsea player, Nicolas Jackson.
Bayern Munich are the current frontrunners to sign the 24-year-old, though no deal has been agreed with Chelsea prepared to wait on possible late interest from Newcastle, should they sell Alexander Isak.
Villa had been pushing for a loan deal but the £10m fee being asked by Chelsea is currently beyond their means, due to the need to comply with Uefa’s financial fair play rules.
Those constraints make big money signings a non-starter, with reported interest in Borussia Dortmund attacker Max Beier believed to be wide of the mark.
A loan return for Marco Asensio remains possible if Villa can strike an agreement with Paris Saint-Germain in the final days of the window.
The club are prepared to push their business as late as possible in the hope deals become more affordable as the deadline nears.