The 21-year-old's loan move to Nottingham Forest was a hugely successful one, as he played a key role in earning Steve Cooper's side promotion to the Premier League.
Spence produced two goals and five assists from 45 Championship appearances in the 2021-22 season, as well as finding the back of the net against Leicester City in the FA Cup.
The defender has since returned to the Riverside Stadium, but he is seemingly set to depart this summer amid interest from both North London clubs.
Arsenal and Spurs have been tipped to do battle for the England Under-21 international, whose contract at the Riverside Stadium expires in the summer of 2024.
However, Antonio Conte's side have stolen a march on their bitter rivals in the race for Spence, but reports of a £20m deal being agreed are now thought to be wide of the mark.
According to Sky Sports News, Tottenham chairman Daniel Levy is set to step up the club's pursuit of Spence in the coming days as Fabio Paratici works on incomings elsewhere.
The report adds that Tottenham were initially prepared to pay in excess of £10m for Spence, but Forest are holding out for a guaranteed fee of £15m, which led to a breakdown in talks the first time around.
Spence himself is said to be keen to make the move to the Tottenham Hotspur Stadium, as the Champions League contenders aim to increase the youthful English talent within their ranks.
Spence joined Middlesbrough from Fulham in the summer of 2018, and the defender has gone on to score two goals in 70 outings for the Riverside club in all tournaments.
The 21-year-old's arrival could pave the way for Emerson Royal to leave the club, with the Brazilian thought to be surplus to requirements under Conte after a tough debut season.
Atletico Madrid supposedly hold an interest in bringing Emerson back to La Liga, and the former Barcelona man had previously claimed that Diego Simeone's side were keeping tabs on his situation.
Tottenham have already bolstered their wing-back ranks with the signing of Ivan Perisic on a free transfer from Inter Milan, and the Croatian is one of three early signings at Spurs.
Fraser Forster and Yves Bissouma have also penned deals with the Lilywhites, and Conte is still thought to be after a new striker and centre-back before the window shuts.
Spurs could have also been handed a boost in their efforts to bring Christian Eriksen back to the club, as the Denmark international has reportedly turned down the chance to move to Manchester United.