If Spurs submit a 30-million-pound offer to Manchester United this off-season.
The England forward had hoped to secure a permanent switch to FC Barcelona after an impressive loan spell, during which he contributed 14 goals and 14 assists as the Catalan club claimed the La Liga title. However, Barcelona opted to pursue Anthony Gordon instead, leaving Rashford's long-term plans up in the air.
According to talkSPORT reporter Alex Crook, United are still expected to place Rashford on the market before the transfer window closes. Crook added that the 28-year-old is eager to move on, although he does not expect Arsenal to enter the race for his signature.
"I think if he goes anywhere in London, I'm keeping an eye on Tottenham," Crook said.
"I could see that deal happening. Roberto De Zerbi believing that he can get the best out of Marcus Rashford.
"When you say a cheap deal, I think probably an offer of 30million will be accepted by Manchester United, but you have to factor in he's on 325,000 a week at Old Trafford, and doesn't seem too willing to take a pay cut."
Recent reports have indicated Rashford is due back for Manchester United's pre-season preparations following his post-World Cup break.
There is also said to be a willingness from both manager Michael Carrick and the forward to work together if he remains at Old Trafford.
Even so, both parties could still favour a transfer should a suitable opportunity arise. United are reportedly keen to reduce their wage bill, with Rashford's salary viewed as a significant financial burden.