The 29-year-old is available on a free transfer after a four-season stay at Bournemouth and has been reviewing multiple offers since the season ended.
Sky Sports News understands the prospect of staying in the Premier League and a move to London is something he has long been keen on.
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LaLiga and Serie A sides have tabled offers but Spurs look to have won the race for the Argentina International.
Senesi played 128 times for Bournemouth in all competitions, scoring six goals and providing 10 assists.
Could Robertson follow?
Latest from Sky Sports News' Michael Bridge:
Spurs are also hopeful Andy Robertson will finalise a move after leaving Liverpool.
Spurs tried to sign the left-back during the January transfer window but he ultimately stayed at Anfield.
However, Robertson will depart Liverpool on a free transfer this summer and Spurs are again pursuing his signing.
Despite late interest from Juventus, there is optimism a deal will be completed before Robertson captains Scotland at the World Cup.
And will Tel stay?
Latest from Sky Sports News' Zinny Boswell:
Mathys Tel would ideally like to stay at Tottenham, Sky Sports News understands, after overcoming a difficult season to play a decisive role under Roberto De Zerbi in helping secure their Premier League survival.
The 21-year-old's priority is to be in a stable environment moving forwards where he feels the trust and confidence of the club.
In 18 months at Spurs, Tel has worked under four different head coaches while the club have suffered consecutive 17th-place finishes.
Tel has faced unique challenges at Spurs this season. He was overlooked for the initial Champions League squad by Thomas Frank, then brought back in December to replace Dominic Solanke, only to be removed again in January when the striker was fit.
The uncertainty around his place in the team created significant speculation about his future and an intense winter for Tel amid strong interest from clubs in Europe.
Tel has played his best football at Spurs under De Zerbi. He earned the Italian's trust with his performance off the bench at Wolves in late April.
He won the corner at Molineux which led to Joao Palhinha's goal and Spurs' first league win of 2026, chasing down what had appeared to be a lost cause with time running out.
It proved a turning point for both club and player. The Frenchman started the remaining four games on the left, contributing a goal and an assist that proved crucial in Spurs avoiding relegation.
Tel's goal in the 1-1 draw with Leeds was overshadowed at the time because he gave away the penalty for the equaliser. However, De Zerbi supported Tel after his error and continued to select him for the most important games of the season.
It has been a long season for Tel, which began with him being subjected to racial abuse on social media after missing a penalty in Spurs' Super Cup final shoot-out defeat to PSG - an incident understood to have deeply affected him emotionally.
The 21-year-old has been through a lot this season and feels he is approaching a crucial stage in his career where he needs the right conditions to progress. He hopes that will be at Spurs under De Zerbi.
