The two English giants are currently preparing to get their Premier League campaign underway with fixtures against Fulham and West Ham United respectively.
Jurgen Klopp and Pep Guardiola have also acted swiftly in the transfer market, the indication being that their respective business is complete aside from City wanting to sign a new left-back.
However, according to Fichajes, Liverpool and City are among a number of clubs who are monitoring any developments with the future of Pino.
The 19-year-old is tied to the Yellow Submarine until 2027, the latest contract extension being penned as recently as last winter.
Nevertheless, it appears that Klopp and Guardiola are admirers of the prospect and could make an approach in one of the upcoming transfer windows.
Despite not being due to turn 20 years of age until October, Pino has already made 77 first-team appearances for the Spanish outfit.
A total of 14 goals and five assists have come during those outings, Pino providing 10 contributions during the most recent La Liga campaign.
The versatile playmaker, who has already earned four caps for Spain, is expected to continue in a senior role for Villarreal during 2022-23.
However, boss Unai Emery will be inevitably wary of any bids for one of his key men, whose release clause is allegedly set in the region of £67m.
Chelsea and Arsenal are also said to be monitoring the situation but a bid from either club is unlikely to come before the start of September.
The Gunners have already invested heavily in their first-team setup with a central midfielder currently the priority for Mikel Arteta.
Meanwhile, Chelsea have instead committed to trying to wrap up a deal for 18-year-old Aston Villa playmaker Carney Chukwuemeka, who is expected to complete a move to Stamford Bridge later this week.