Lambert was Saints' top scorer in the Premier League last season after netting 15 times, but he has been linked with a reunion with former manager Nigel Adkins at Reading.
West Ham United are also reported to have shown an interest in the 31-year-old, but Pochettino is adamant Lambert is a key part of his plans for the coming season.
"We count on Rickie," said Pochettino in the Daily Echo following the weekend friendly against Besiktas.
"We are happy with him. I didn't know there was any interest in him. This is a surprise for me."
Uruguay attacker Ramirez only joined Southampton 12 months ago from Bologna and scored five goals in the Premier League last term.
He has been linked with a return to Serie A with Inter Milan, but Pochettino is not worried about the prospect of losing Ramirez.
Pochettino added: "I just listen to Gaston. Not his agent. Gaston is happy here and we expect him to stay and to put a lot into the team."