Jose Mourinho was sacked as Red Devils boss on Tuesday, and Pochettino has been widely touted as a potential successor.
However, Emery hinted ahead of Wednesday's north London derby in the Carabao Cup that Pochettino should stay put at Spurs, per Ian Baker of The Independent:
"I think he's very happy at Tottenham. I think he's coaching a very big team with very big players and now they are in the Champions League they are also in a better position in the Premier League than Manchester United.
"I think his performance at Tottenham is very big. I don't know if he's thinking to change for another club, but I am looking at him with a very big commitment to Tottenham, and he's creating a good performance a good idea at Tottenham. Tottenham improved a lot with him."
Pochettino, 46, has been in charge at Tottenham since 2014 and has overseen three consecutive top-three finishes in the Premier League.
Spurs are now also well established as a UEFA Champions League side and have made it through to the knockout rounds for the second year running.
As a result of his success with Spurs, Pochettino was being linked with United even before Mourinho was sacked, and now he is being widely tipped to take over at Old Trafford in the summer, as Bleacher Report's Dean Jones noted:
Despite United's status as one of the world's biggest and most successful sides, the vacant manager's job is not necessarily the most attractive.
Since Sir Alex Ferguson left the club in 2013, United have been unable to maintain anything close to a genuine title challenge, and their status in Europe has declined.
There is an argument that Pochettino would be better off staying at Spurs:
Spurs are currently third in the Premier League and are on the verge of moving into a new stadium, while United are 11 points off the top four in sixth and look a shadow of the club that dominated the English top flight for so long.
However, the Red Devils do have the prestige and financial clout to persuade Pochettino into a move even if Spurs look a better place to be.