The Saints boss has played down rumors linking the duo with moves away from St Mary's Stadium, as they are both integral to his plans for the upcoming Premier League season.
Lambert netted in a 3-1 friendly win over Turkish side Besiktas on Saturday, after finishing as the club's top scorer in the Premier League last season with 15 goals. Pochettino was quick to highlight the 31-year-old's importance to Southampton, amid reported interest from West Ham and the striker's former boss, Nigel Adkins, at Reading.
"We count on Rickie," Pochettino told the Daily Echo after Saturday's victory. "We are happy with him. I didn't know there was any interest in him. This is a surprise for me."
Ramirez has already been linked with a return to Serie A with Inter, just one season after his 12 million pound switch from Bologna.
The Uruguayan's agent, Pablo Betancourt, says that his client would consider a move if Inter made a concrete approach, but Pochettino is not worried about the prospect of losing the attacking midfielder, who scored five goals in 26 appearances for the Saints last season.
"I just listen to Gaston, not his agent," Pochettino said. "Gaston is happy here, and we expect him to stay and to put a lot into the team."