The former Barcelona head coach is expected to take a break from football in the coming months but he is open to a club return ahead of the 2023/24 season.
Reports from Diario AS claim Atletico are targeting Enrique as their first choice option, if Simeone steps away from the club, with his contract running until 2024.
Simeone has transformed Atletico since his appointment in 2011 but there is a growing sense of the former Argentina international reaching the end of his time in Madrid.
Atletico will leave the decision up to Simeone, due to his iconic status at the club, but CEO Miguel Angel Gil Marin has hinted at an interest in Enrique.
“I really like him personally and professionally. I think he has the talent to coach any team in La Liga”, he said.
“It’s clear he adds up for everyone. For the media, the players and for the clubs, because he offers a high level of performance.”