The Spurs midfielder was linked with a switch to Old Trafford only for Jose Mourinho to sign Nemanja Matic from Chelsea instead.
And Anderton thinks Dier may have been right to want a move if he doesn’t get regular playing time at Wembley this year.
The former England international explained to sportingbet.com: “Eric could have quite easily gone to United this year, but Levy made sure that didn’t happen, but he’ll want to play.
“He won’t kick up a fuss, but if he can go and be a regular in another team you couldn’t blame him for leaving – no matter how much he loves the club.
“He had a fantastic year before Victor Wanyama came in, so I thought the signing of Wanyama was harsh.
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“Eric could have quite easily gone to United this year, but Levy made sure that didn’t happen”
Tottenham hero Darren Anderton
“As a player if you have a great year, you should be rewarded for that but Pochettino went out and bought Wanyama, which he probably sees as a bit of a kick in the teeth.
“Dier has got on with it though, which has meant he has been used as more of a utility player, which isn’t great for his career. Wanyama was brilliant last year so you can’t argue too much with the Pochettino.
“Dier wants to be a defensive midfielder and after playing so well for England in that position, he won’t want to play centre back, he’ll want to be a defensive midfielder.”
Dier has played in both of Tottenham’s first two Premier League matches of the season.
Tottenham return to action on Sunday against Burnley with the match getting underway at 4pm.