The 21-year-old is reportedly one of Diego Simeone’s requests to strengthen Atleti’s right side next season.
Chukwueze has a €100m release clause at Villarreal, but a bid of €50m should be enough to sign him.
He has made 32 La Liga appearances for Yellow Submarine this season, with a return of three goals and four assists.
Signed from the Diamond Football Academy in Nigeria, Samu has risen through the ranks at Villarreal.
Leading Premier League clubs were linked with the promising winger earlier this year.
Chukwueze has been capped 12 times by Nigeria and featured in the 2019 African Cup of Nations.