The Uruguayan has yet to justify his £12million price tag after arriving from Bologna in the summer of 2012 and reports suggest he is growing unsettled at St Mary's.
Ramirez's representative has previously suggested the player did not like Pochettino and this week suggested Inter Milan were interested in the attacking midfielder - talk the Saints boss played down ahead of Saturday's trip to Arsenal.
"Gaston knows perfectly what I think and I know what he thinks," he said. "That's a private matter between us. He is fully obliged to fulfil his contract.
"That's all he has to do as a Southampton player. He has to work in order to fulfil that contract and be part of the team."
Pochettino does not expect to be busy when the transfer window opens again because of the players being produced by their academy.
Gareth Bale, Alex Oxlade-Chamberlain and Theo Walcott are three of the most famous names from the club's production line, with Adam Lallana the latest graduate to receive a senior international cap.
The Saints captain has played a starring role this season and is one of 12 players from the youth system to have featured in their matchday squad.
That conveyor belt of talent makes Pochettino, whose side sit third in the Premier League standings, confident about the future amid questions over the depth of his squad.
"We don't see that as a problem," the Saints boss said. "We have a lot of young players coming from the academy that are pushing really hard.
"They are making a case for being in the senior team. Players like Sam Gallagher and Harrison Reed, very exciting players.
"So in that sense we are not worried about the depth of our squad because we have a lot of young players that guarantee us a very good future in the immediate future.
"We are covered in that sense so we are not worried."
Southampton's focus on home-grown talent is an unusual one in the richest league in the world, but one increasingly pointed to as the way to go.
Luke Shaw and James Ward-Prowse have flourished after being brought into the first-team, while several others have been given Premier League experience as teenagers.
"I think there's great talent in English football academies, as much as in Spain, Brazil or Argentina," Pochettino said. "It all comes down to individual decisions. Every club makes their own decisions.
"But overall I would say the Premier League is financially the most potent league in the world.
"Most of the time it is much easier to sign a player who is the finished product, probably from abroad, instead of using younger players and giving them confidence, time and the possibility of coming through the ranks and be part of the senior side.
"It is understandable because managers depend on results of every single game.
"What's been the case here in Southampton is that two good things have come together - the fact that there's been a very good project in place for a long time, in the sense that we always push players through the academy, and a manager that fully believes in young players and wants them to come through the ranks."