Speculation in the Boxing Day papers claimed United manager David Moyes was considering a £15million January bid for Lallana.
The 25-year-old has been an impressive figure for Southampton this season and again caught the eye in Thursday's 3-0 victory away to Cardiff City.
He created the opening goal for Jay Rodriguez and his performance capped a memorable few days after he got married earlier this week.
Saints boss Pochettino is not worried about losing the England international and is confident Lallana is happy to stay 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 made over 240 appearances for Southampton after coming through the ranks and was rewarded with his England debut against Chile last month.