According to The Times, Spurs were hopeful of landing the England international in a bid to help him rediscover his best form.
The 24-year-old has fallen out of favor for club and country following a dreadful 2021/22 campaign.
Rashford managed just five goals in all competitions after the beginning of his season was disrupted by a serious shoulder injury.
However, it is understood Rashford, who has one year left on his Old Trafford contract, has decided to stay and try to impress incoming United manager Erik ten Hag.
The United forward had established himself as one of Europe’s most exciting young players before the prolonged dip in form.
Tottenham are looking for a versatile forward who can play across their front three – and the Times also reports they have been offered Gabriel Jesus by Manchester City.
He has the attraction of being English, to help Tottenham meet the quota of home-grown players, and has one year left on his contract. However, Spurs were told that Rashford would like to stay at United and try to impress Erik ten Hag, who has arrived as head coach.
Rashford scored 56 goals and set up another 37 in the three seasons before a miserable 2021-22, despite carrying a number of injuries. Getting a fair run out under new management could do him well, but his contract and rumors of potential moves elsewhere won’t be going away anytime soon if he doesn’t rediscover form.