United boss David Moyes has been linked with a £15million swoop for Saints captain Lallana in January after the 25-year-old's impressive opening to the season, scoring four goals and assisting five already.
The England international, who got married earlier in the week, was again a key player in Southampton's 3-0 win at Cardiff on Boxing Day, setting up Jay Rodriguez for the openinggoal.
But Argentine tactician Pochettino insists he is under no pressure to sell Lallana and is confident he will remain at St Mary's.
"I think Adam and other players are going to stay with us," said Pochettino after the win at Cardiff.
"There is no pressure to sell them, Adam has said he is happy at Southampton and Southampton have no plans to sell him."
Of Lallana's wedding, he added: "He has had a complete week.
"He trained yesterday, then went off to get married and then went back to training. He did not even have a day off."
Lallana has featured over 240 times for Southampton, scoring 52 goals during that period, after rising through the ranks and was rewarded with his England debut against Chile last month.
Southampton manager Mauricio Pochettino is not looking for new signings during the January transfer window.
Pochettino improved his squad during the summer by spending big to sign defender Dejan Lovren, midfielder Vincent Wanyama and striker Dani Osvaldo.
The Argentinian has been rewarded with a fine first half of the season, which saw Southampton challenge at the top end of the table before slipping back to ninth in recent weeks.
And, rather than pep up his squad with fresh additions in the New Year, Pochettino will instead put his faith in the young players already at his disposal at St Mary's.
"We're not really concerned with the transfer window," said Pochettino ahead of Sunday's game against Everton.
"We're really happy with the young players that are part of this team.
"We're really happy that they are partaking in training sessions with the older players and that they're getting a feel for what it is to be in the senior side.
"That gives us a very important equilibrium, a balance in the team, and we're really happy with their contribution, so we're not really looking at the transfer window."
Ince is out of contract in the summer, I believe. I think he could fit right in and give as an extra option in the attack.
Sadly can't see this now.
Ince is out of contract in the summer, I believe. I think he could fit right in and give as an extra option in the attack.
Southampton have enquired again for Cagliari's defender Astori
from Tancredi
It's that deja vu feeling all over again.