World Cup winner Pogba announced his desire for a "new challenge somewhere else" in June and has been heavily linked with a transfer to former club Juventus and Real Madrid.
The Frenchman has struggled to live up to expectations since arriving at Old Trafford from Juve in August 2016 for £89million, then a world-record fee.
Pogba was still included in United's squad for their pre-season tour to Australia and Asia, with manager Ole Gunnar Solskjaer hopeful of retaining his services.
Mata also wants Pogba to stay put and help unify the team.
"We all know Paul and he is a fantastic midfielder, and a very good guy, very positive, and a good influence for everyone," said Mata.
"I think he is happy and brings everyone together, but I cannot speak for other people - I speak for myself.
"As a team-mate and a friend I would like him to stay and be happy because he is a very good player for us."
David de Gea looks set to continue his career at United, as he is reportedly ready to sign a six-year contract extension.
"David is the best goalkeeper in the world and one of my best friends so I want him to stay," said Mata.
"On a professional level, it would be great if he stays because he will give us many points over the next season, so I'm very happy if he stays."