The 22-year-old Spaniard has struggled to settle at the north London club and has been sent out on loan stints to Spain.
Tottenham paid Sevilla £21.6m plus added Erik Lamela as a part of the deal to bring Gil in 2021.
The Spaniard is set to be back in north London this summer following the end of his loan spell at Sevilla, but he could be sent out on a temporary move yet again.
Lazio are looking at wingers and, according to Italian radio station Radiosei, Gil is on their radar.
It has been claimed that coach Maurizio Sarri and the club’s president Claudio Lotito have identified candidates for their requirement for a winger in the summer.
Gil has played 35 matches this term in all competitions making six-goal contributions during the process.
Tottenham Hotspur are suggested to want €30m for Gil if they agreed to sell him this summer.
It is unclear what plans new Tottenham boss Ange Postecoglou has for Gil.
