Gomes is currently on loan at Goodison Park from Barcelona, joining from the Catalans last summer.
He has impressed on Merseyside, becoming a crucial part of Marco Silva’s team and going a long way to rebuilding his reputation after a disastrous time at the Nou Camp.
Everton’s intent is to try and turn his move into a permanent one this summer, with reports suggesting Barcelona will ask for £30 million.
However, they are facing competition from across Europe for the Portugal international’s signature, and now it seems there are rivals in the Premier League too in the form of Tottenham.
Spurs are expected to make money available to Mauricio Pochettino this summer, with funds freed up following the completion of their new stadium.
Pochettino is mainly looking to add to his midfield after Moussa Dembele left for China in January and has identified Gomes as a potential replacement for the Belgian midfielder.
The 25-year-old is a player he has considered signing before and has monitored him regularly over the past 18 months. The Spurs boss even had him scouted during the Merseyside derby back in December.
It is Spurs belief that Gomes could prove to be a bargain at £30 million, a relatively low price given the inflated transfer fees in the market at this moment in time.