Earlier this month Lyon's Dejan Lovren arrived for £8.5million and there is clearly still money in the bank for signings at St Mary's.
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."
Celtic, meanwhile, lost their opening pre-season match 1-0 to Ukrainian side Sevastopol on Wednesday night but will look certain to add a defender to their squad.
Former Hull and Wolves defender Steven Mouyokolo spent a week training with Celtic at the end of last season and played last night as a trialist.
A slip by Fraser Forster in the 65th minute allowed a free kick from Kostiantyn Iaroshenko to find the net, with the Hoops unable to find an equaliser as Virgil van Dijk and Amido Balde made their Celtic debuts.
Mouyokolo had a steady match in the centre of defence alongside Van Dijk during the first half before being joined by Kelvin Wilson after the break.