The 23-year-old spent the second half of the 2023-24 campaign on loan at Genoa, representing the Italian outfit on 16 occasions in all competitions.
Spence has another three years left to run on his contract at the Tottenham Hotspur Stadium, but he is being heavily linked with a permanent move away from his parent club.
According to Italian journalist Fabrizio Romano, Spurs are in discussions with Genoa over a long-term switch for Spence, who is not in the plans of Tottenham boss Ange Postecoglou.
The defender has only made six appearances for his North London club since arriving from Middlesbrough in the summer of 2022.
Meanwhile, according to Corriere di Roma, Roma are exploring the possibility of signing experienced defender Mats Hummels on a free transfer this summer.
The 35-year-old was in impressive form for Borussia Dortmund during the 2023-24 campaign, making 40 appearances in all competitions, including 13 outings in the Champions League as BVB reached the final.
Hummels's contract is due to expire at the end of June, though, and there is currently a host of speculation surrounding his future.
Roma are said to view Hummels as a leading target this summer, with AC Milan also believed to be keeping a close eye on his situation in Germany.
A number of clubs from Saudi Arabia and the MLS are said to be keen on the defender, but he allegedly wants to continue his career in European football.
Hummels started his professional career at Bayern Munich back in 2006, and he has made almost 700 club appearances, in addition to being capped on 78 occasions by Germany.
Elsewhere, Real Zaragoza are reportedly battling to re-sign Ander Herrera this summer.
The Spaniard came through the youth system at Zaragoza before progressing to first-team level in 2009, and he represented the club on 86 occasions before leaving for Athletic Bilbao.
Herrera made 128 appearances in his first spell with Athletic before moving to Manchester United, featuring on 189 occasions for the Red Devils, ahead of a switch to Paris Saint-Germain.
The 34-year-old headed back to Athletic in August 2022, making 48 appearances in his second spell with the club, but his contract is due to expire at the end of June.
According to Mundo Deportivo, Zaragoza are leading the race to sign him on a free transfer this summer.
Herrera made 27 appearances for Athletic during the 2023-24 campaign, including 23 outings in La Liga.