The Premier League outfits will look for more transfers as the season progresses.
Pep Guardiola and Jurgen Klopp already have their sights on a deal for the young playmaker.
According to Fichajes, City and the Reds have been left encouraged by the development of Baena, who is yet to make a start for Villarreal in La Liga this season, has already chipped in with three goals.
The Yellow Submarine remains in a strong position with regards to Baena’s future, his contract being due to expire at the end of 2024-25.
However, there is thought to be a €35m release clause in Baena’s deal, something which could be exploited if the 21-year-old continues on his current trajectory.
The La Liga outfit are reportedly keen to hold discussions with the youngster.
The report adds that City and Liverpool are expected to step up their interest if Baena performs at a high level on a regular basis.