The 24-year-old was again in impressive form for his Italian club during the 2021-22 campaign, scoring 25 goals and registering four assists in 49 appearances in all competitions.
Meanwhile, he has scored 74 goals and registered 24 assists in 180 outings for Inter since making the move to San Siro from Racing Club in July 2018.
Martinez only signed a new long-term deal with Inter in October 2021, with his current deal due to run until June 2026, but there remains speculation surrounding his future.
According to journalist Alfredo Pedulla, the Argentina international is happy in Milan and wants to remain with the club on a long-term basis.
Inter are also allegedly keen to keep hold of the forward, but Tottenham are said to be lining up a €90m (£77m) bid for the South American, which will have to be taken seriously by the club.
The Italian giants are also expected to be well-stocked in the final third next term, with Paulo Dybala set to arrive on a free transfer from Juventus.
Meanwhile, Simone Inzaghi's side are in talks with Chelsea over the return of Romelu Lukaku, who could head back to the club on loan for the 2022-23 campaign.
Barcelona, Manchester United, Real Madrid and Manchester City are also among those believed to be admirers of Martinez due to his form since arriving in Italian football.
Tottenham had to fight to keep hold of Harry Kane during last summer's transfer window, with Man City offering in excess of £100m to sign the England captain.
However, there is not expected to be a transfer saga involving the 28-year-old this summer, as he is said to be happy at the club under head coach Antonio Conte.
Spurs will be back in the Champions League next season after securing a top-four finish in last season's Premier League table, while they have already been busy in the transfer market.
Ivan Perisic's arrival on a free transfer has been confirmed, while Fraser Forster has joined from Southampton, and a deal for Brighton & Hove Albion's Yves Bissouma is said to be imminent.
Conte's side will open their 2022-23 Premier League campaign at home to Southampton on August 6 before travelling to Stamford Bridge to face Chelsea one week later.