The 19-year-old has accepted a £20,000-a-week contract offer to move to White Hart Lane after his contract with United expired this summer and he refused to sign a new deal as they would not meet his wage demands.
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The Red Devils are entitled to compensation as they brought Fryers through their youth system, but the fee will be decided by an independent tribunal as the Old Trafford club want £6 million for the left-back while Spurs rate him at around £2m.
Fryers is understood to have been told that he will go straight into the Spurs first-team squad under new head coach Andre Villas-Boas as competition for Benoit Assou-Ekotto, with Danny Rose likely to leave the Londoners this summer.
The defender, who broke into Sir Alex Ferguson's first-team squad last season, will join Ravel Morrison and Paul Pogba as the latest promising youth prospect to turn his back on the club.
Sir Alex has already expressed concerns over the full-back’s future, admitting that the club had not been in contact with him during the post-season break.
"We haven't heard anything from Zeki Fryers," said the United boss to MUTV on Monday. "I don't know what's happening there but he's not been in touch with the club. His agent hasn't been in touch with the club and I can only assume he'll be back for training."
Fryers made his debut in the Red Devils’ 3-0 victory over Leeds in last season's League Cup but has not appeared in the Premier League since his side’s Boxing Day defeat to Blackburn.
The move will signal a third high-profile departure of United's brightest young talent in half a year, with Morrison having joined West Ham in January and Pogba moving to Juventus on Tuesday.
Ferguson accused Pogba of showing the Old Trafford club “a lack of respect” following his switch to the Turin giants, with the Frenchman having been locked in a contract dispute with United for a number of months.