Saints are deciding whether to increase their offer for Sam Byram after having an initial bid turned down by Leeds.
The 20-year-old right back, who has come through the ranks at Elland Road and broke into the first team at the start of 2012/13, was the subject of an offer in the region of £4.5m.
Saints are looking for back-up to Nathaniel Clyne after selling Calum Chambers to Arsenal for £16m.
But there is serious doubt as to whether the club will want to offer more for Byram, who has made 70 Championship appearances for Leeds, with several other right back targets also being considered.
When asked about the Byram bid, Ronald Koeman said: “We are after that, we lost Chambers to Arsenal, it was a player we had on the list and it’s true that we had a bid for him, yes.
“What I heard was that Leeds didn’t accept it.”
On the potential of another offer, he replied: “I don’t know. I am not doing the bids for players.”
Koeman again reiterated the club’s interest in left-sided centre halves Marcos Rojo of Sporting Lisbon and Steaua Bucharest’s Florin Gardos.
However, deals have yet to be struck for either of them to come in and fill the gap left by Dejan Lovren.
“That’s true, we are interested because we lost Lovren and we need a player in that position. These are two players who are very interesting for us,” said Koeman.
Rojo, 24, has previously been linked with Liverpool, Chelsea and Juventus this summer after impressing in the World Cup for Argentina.
Gardos, 25, has won 12 international caps for Romania after making his debut three years ago.
Meanwhile, Koeman also reiterated the club’s stance over Morgan Schneiderlin, who was left out of the weekend friendly against Germans Bayer Leverkusen as he continues to push for a move to Tottenham and a reunion with Mauricio Pochettino.
Saints do not want to sell the midfielder – having already sold five players for big money this summer – and are waiting to see how he handles a return to training today.
“His future is in the club, he is a player of Southampton and Monday morning there will be the next training session,” insisted Koeman.
“We expect him for that training session and he will continue like the player that he was in the past, and nothing more.”
Koeman also admitted he is pleased to generally be answering more questions on signings than sales at the moment.
“It’s always nicer,” he smiled.
“Sometimes you need players who move because it brings a new ambition in the team.
“We lost a lot, but we’ve brought some in.”