Spurs boss Jose Mourinho has watched the 25-year-old for a number of years and is a big fan of the Slovakian defender.
SunSport understands Skriniar is keen on a move to the Premier League, and would be interested in linking up with Tottenham.
But Inter are demanding a hefty fee for one of their prize assets, money which Mourinho is not prepared to pay.
Spurs would be willing to fork-out between £25m and £30m for the centre-back, with discussions set to continue through the weekend.
It is understood Skriniar’s agent is in Milan, and is holding talks with Inter over the ex-Sampdoria star’s future and plans to move away.
The Nerazzurri could use the cash made from him to launch an assault for Manchester United outcast Chris Smalling.
Antonio Conte is a fan of the 30-year-old England defender, who is training alone at Carrington while his future is decided.
The ex-Fulham ace is also being chased by Roma, where he had a successful loan spell last season in Serie A.
Another defender Conte has an eye on is Antonio Rudiger, with the Chelsea ace considering his future at Stamford Bridge.
The Germany international has been left out of both Frank Lampard’s starting elevens so far this season, and has been left frustrated.
Inter are also keeping tabs on Blues duo Marcos Alonso and Emerson Palmieri this summer.