Luke Shaw, Adam Lallana and Rickie Lambert have all been linked to transfers this January.
But Pochettino says they will stay and rumours that club-record striker Dani Osvaldo is unsettled and will head back to Italy are untrue.
“He’s happy here and very content,” Pochettino told BBC Radio Solent.
Italian Osvaldo, 27, joined the club for £15m in October, scoring three goals in 13 appearances and has been linked with a move to Roma and Inter Milan.
Pochettino, who arrived on 18 January last year, has been linked with a move to Italy, but also brushed off those reports.
“There are so many rumours coming out of Italy that if we listened to all of them we would go mad,” he said.
“Obviously the adaptation process (for Osvaldo) is not easy and is taking it’s time.
“He has had some illness and some injury, so we are just waiting on his suspension to end so he can play some games for us.”
Defender Shaw, midfielder Lallana and striker Lambert continue to be linked to other Premier League clubs.
Shaw is rumoured to be interesting Chelsea, Lallana is being linked to Manchester United and Lambert to West Ham, but Pochettino says the club want to keep them.
“There is no intention for the club to sell them,” he said.
“Rumours can happen, especially at this time of the year, but we cannot do anything to stop that, it is what basically happens. We will keep on working and doing what we do.”
Written by Steve Milne