The Saints have already made a move to prepare for their second season in the Premier League with the arrival of Lyon's Dejan Lovren for £8.5m last month.
And with the club back in pre-season training, Pochettino confirmed a move for Celtic midfielder Wanyama "could happen" still, while there is interest in Valencia's Banega and Brazil international Damiao.
"We manage a lot of information about very good players," the Saints boss said. "One of them is Damiao, also Banega and also Wanyama.
"We are managing the situation as well as we can at the moment.
"The main thing is that we as a club, Southampton, are managing when these negotiations happen so that is what is happening.
"We are managing when these players are going to be signed and how we sign them.
"Our goals are very clear. I am also not trapped by the fact that I said I wanted to have our transfer window closed by July 1.
"We are not interested in 15 or 20 players. We are interested in maybe two or three key players.
"At the same time, I also want to say our squad at the moment is really good and it is not like we are trapped in the sense that we need these players to be a better squad.
"Our squad as it is really good already, but we just want to bring in two or three players that reinforce key areas in the squad to become an even better team."