Dier, 23, was heavily linked with a move to Old Trafford during the summer transfer window but the move failed to materialise, with Spurs adamant that the versatile defender would not be sold at any price.
Pochettino said United made their initial approach for Dier last season and revealed that he was unhappy with Red Devils manager Jose Mourinho for having a post-match conversation with the defender after Spurs' defeat at Old Trafford in December 2016.
"Mourinho and I had finished our interviews at Old Trafford and the players were doing their warm-down on the pitch," Pochettino wrote in the Daily Mail. "When Jose was done with the press, he stood by the entrance to the tunnel and regarded the returning players.
"He greeted Moussa Sissoko and hugged Dier. They passed by me en route to the dressing rooms, laughing, speaking in Portuguese. Maybe it is a common Mourinho tactic, but he put Eric in a compromising position. You cannot do that after a defeat."
Pochettino added that he and Dier continued to have disagreements on the latter's best position, with the former Espanyol boss insisting that the 23-year-old has the potential to be the best centre-back in the Premier League, while the England international is more keen on playing as a defensive midfielder.
The Argentine coach also revealed that Dier was unhappy with the signing of Victor Wanyama from Southampton last summer as he felt that the move threatened his place in the Spurs midfield.
"I've told Eric he has what it takes to be the best English centre back but he has to be convinced of that himself," Pochettino wrote. "We've put the conditions in place for him to improve."
Dier has featured in all nine of Tottenham's league games this season, including a substitute appearance in the club's 4-1 win over Liverpool on 22 October.