The Red Devils have been linked with the 25-year-old as they look to overhaul their squad this summer.
Ole Gunnar Solskjaer has already added Daniel James and Aaron Wan-Bissaka to his ranks but more signings are expected.
Lemina impressed for Southampton last season, although he was limited to 21 Premier League appearances due to injury.
But the Manchester Evening News claim United and Ed Woodward are not interested in the Gabon international.
That’s because the Red Devils believe they are being linked with the player to set up an auction for the Saints player.
Lemina could leave the club for about £30million, according to reports.
And the midfielder hasn’t travelled with the rest of the squad to Austria for their pre-season as a transfer looks increasingly imminent.
Arsenal and Manchester United have both been linked with Lemina as they are known to be in the market for a new man in the middle of the park.
The Gunners have lost Aaron Ramsey to Juventus while United have seen Ander Herrera exit for Paris Saint-Germain.
And the future of Paul Pogba at Old Trafford also remains up in the air with Real Madrid and Juventus interested in the World Cup winner.
Solskjaer has insisted the central midfielder won’t be leaving this summer though.
“Agents talk all of the time and, as I said, we’ve not had any bids, from any clubs, that’s all I can say about this matter,” Solskjaer said.
“I’m not just talking about Mino Raiola, there are loads of agents out there, they have got clients that they are looking after, so they can look after their clients.
“As long as they [players who want to leave]’re here, they’re professionals, working, giving everything they’ve got, agents and everyone else can talk.
“And we’ve got our own talks behind the scenes and I’m not going to tell you what we’re talking about, as you would probably imagine.”
United have their first match of pre-season on Saturday against Perth Glory at midday UK time.