The 19-year-old enjoyed an impressive 2021-22 campaign for the Yellow Submarine, scoring seven goals and providing four assists in 31 appearances across all competitions.
Pino extended his contract with the La Liga side in November last year until the summer of 2027, but that has not stopped the rumour mill from linking the winger with a potential exit.
A recent report claims that both Liverpool and Man City are among a number of European clubs who are closely monitoring Pino's development at Villarreal.
The Premier League duo could face competition from Arsenal, however, as AS reports that Mikel Arteta's side are also interested in the Spain international.
The report adds that there is 'strong interest' in Pino from the Premier League which Villarreal were not anticipating in this summer's transfer window.
Villarreal are keen to keep hold of Pino, but they may consider cashing in on the winger if they receive a significant offer from an interested club, as they look to balance their books.
Unai Emery's side have only spent around £800,000 on full-back Kiko Femenia so far this summer, but the Yellow Submarine are reportedly targeting a double swoop for Tottenham Hotspur duo Giovani Lo Celso and Tanguy Ndombele.
Lo Celso, who spent the second half of last season on loan at Villarreal, is set to join the club on a permanent deal, according to journalist Fabrizio Romano.
Ndombele, meanwhile, is surplus to requirements under Antonio Conte and Villarreal are believed to be interested in taking the Frenchman on a season-long loan deal.
The addition of two Spurs players at Villarreal could therefore allow North London rivals Arsenal to move for Pino, who is understood to have an €80m (£67.3m) release clause in his contract.
The Gunners have already spent in excess of £110m this summer, recruiting Gabriel Jesus, Oleksandr Zinchenko, Fabio Vieira, Matt Turner and Marquinhos.
However, Arteta has confirmed that his side remain active in the transfer market and will attempt to bring in some more fresh faces before the September 1 deadline.
"We are going to try. There are a few things we have planned and we are going to try," Arteta told Sky Sports News after Arsenal's opening Premier League victory over Crystal Palace on Friday.
As well as Pino, the Gunners have been linked with the likes of PSV Eindhoven's Cody Gakpo and Leicester City's Youri Tielemans, who are both believed to be valued between £30m and £40m.