The 21-year-old winger has been enjoying a fine loan spell with Elche in Spain’s top flight – where he has been sent from Valencia.
This term is the youngster’s second one at the club, for whom he has made 54 appearances and helped secure promotion to the top tier in the process.
His performances have been earning him rave reviews in his homeland, where he is being tipped to shine in the coming years.
This has alerted Roberto Martinez, who is known to have a good knowledge of his birth country’s football situation.
It is understood the representatives from the blue half of Liverpool have been in attendance for some of Gil’s recent performances, which has fuelled talk of a swoop in the summer.
Everton are thought to be ready to activate his £6.5m release clause, which would render Valencia powerless in the situation.
However, Gil himself is rumoured to be ready to battle for his future at the Mestalla.
The skilful starlet is the latest player to emerge from the Spanish club’s academy set-up – the same one that now Manchester City star David Silva graduated from.