Simeone has previously shown a willingness to sign English players, having brought in both Kieran Trippier and Conor Gallagher in recent years, and is understood to admire the 30-year-old's work rate on and off the ball, reports The Sun.
Any deal faces obstacles, however, with Atletico Madrid already well stocked in attacking areas after adding Lee Kang-in from Paris Saint-Germain this summer, and with Alex Baena, Thiago Almada and Ademola Lookman all also options on the wing. Grealish would likely have to accept a rotation role if a move to the Spanish capital were to materialise.
Grealish has not played since January, when he suffered a foot injury while on loan at Everton, and has been left out of Manchester City's pre-season tour of Asia as he continues his recovery.
He returned to training over the summer and has since been working with RCD Mallorca in Spain to keep himself sharp and raise his profile with potential suitors, having fallen down the pecking order at Manchester City following his £100m move from Aston Villa in 2021.
Should a move to Atletico fail to materialise, a return to Everton remains a live option, with David Moyes' side having seen Grealish contribute two goals and six assists during a productive loan spell before the injury cut it short.
Interest is not limited to Europe, either: Saudi Pro League side Al Hilal have also been credited with checking on Grealish's availability, though the player's own preference is understood to be remaining in English or European football at this stage of his career.
Grealish played a central role in City's treble-winning 2022-23 campaign but has featured only sparingly under Pep Guardiola since, making the coming weeks pivotal in determining where he plays his football once he is fully match fit again.