Liverpool, Arsenal, Everton and Cardiff have all been linked with the Celtic midfielder, but it is Southampton that were given permission to speak to him after a reported £12million bid was accepted. However, Wanyama has so far failed to agree terms with Saints, leading to suggestions of issues with his representatives.
But Pochettino said: "It could happen. We have certain positions that we want to reinforce. I'm confident that our goals will be met."
Pochettino is also targeting big-money moves for Internacional's Leandro Damiao and Valencia midfielder Ever Banega.
He added: "We manage a lot of information about very good players. 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."
Source: PA
Source: PA