While the Saints' outgoing players have dominated the headlines this summer, Koeman has already added seven new faces including Fraser Forster, Shane Long, Graziano Pelle and Dusan Tadic
The Dutchman has been linked with a move for Atletico Madrid's Belgian defender Toby Alderweireld but refused to confirm his interest in the 25-year-old
However, Koeman is confident of landing two targets ahead of Monday's transfer deadline
"I don't talk about names of players," he said.
"In two positions we are trying to bring in new players and we hope to bring (them) in this week.
"The club is doing everything for that and I hope we will finish with that this week."
Saints may have lost the likes of Adam Lallana, Rickie Lambert, Luke Shaw and Calum Chambers but Koeman hopes Jack Cork will not join the exodus.
Midfielder Cork, who has only a year left on his current contract, has been linked with moves to Crystal Palace and Swansea.
The 25-year-old scored his first Saints goal on his 114th appearance in Tuesday night's 2-0 Capital One Cup win at Millwall.
And Koeman insists he wants to keep the former Chelsea youngster at St Mary's, although there are no plans to open talks over a new deal yet
"He's a Southampton player," said Koeman
"There were a lot of rumours but Jack is doing very good and has ambition to stay with Southampton.
"If there is any possibility for him and when he is not happy he knows my office door is open and we can see what is best for everyone in this situation."
But when asked if there were any plans to discuss a new contract for Cork, Koeman added: "Not at this moment."
Cork grabbed the opener with a header after 53 minutes and on a night of firsts, Italian striker Pelle opened his account in stoppage time to give Koeman his first win as Saints boss.
"I was really happy, you know how important it is for strikers to score and it doesn't matter which game it is," Pelle told the club's official website.
"I tell myself if I don't score for two matches in the third I have to
And especially as we didn't win our first two games
Winning is more important than scoring to me."
Source : PA
Source: PA