Spence was one of the breakout stars of England's World Cup campaign, impressing in knockout wins over Mexico, Norway and Argentina, but sits behind Pedro Porro and Andy Robertson in the pecking order at Tottenham.
Manager Roberto De Zerbi is open to selling the 25-year-old this summer as he continues to reshape his squad following back-to-back 17th-placed finishes in the Premier League, with Spence's price tag believed to be around £35m.
Liverpool are understood to admire the versatile full-back, who can play on either side, but at this stage other interested clubs appear to hold a stronger position in the race for his signature.
Those include sides from Italy and elsewhere in the Premier League: Inter Milan held talks over a deal earlier in the summer, while their city rivals AC Milan are also believed to be considering a move.
Spence progressed through Middlesbrough's academy before a loan spell at Nottingham Forest helped force his £19m move to Tottenham, and he has since made over 90 appearances for the club, though increased competition for places has left his long-term future in north London uncertain.
Spurs signed off on Spence's exit as part of a wider reshaping of the squad under De Zerbi, who has already brought in defensive reinforcements this summer and is understood to be relaxed about losing a player who has struggled for consistent minutes. Any deal is likely to hinge on whether a suitor can meet Tottenham's valuation, with the club under no pressure to sell below their asking price given Spence's contract runs until 2028 and his stock has only risen following his performances on the biggest stage.