The Senegal international emerged as a transfer target for the Old Trafford club after they claimed to drop interest in Pedro, with the Spaniard instead moving to Barclays Premier League rivals Chelsea.
Southampton immediately played down reports suggesting United had made an approach for the 23-year-old, who played in their 1-1 Europa League play-off draw with FC Midtjylland on Thursday night.
Louis van Gaal has missed out on a number of main transfer targets this summer and fellow Dutchman Koeman is keen to add Mane to that ever-growing list of names who United have failed to recruit.
“The situation is so easy,” Koeman said.
“We have to deal with that. I don’t like it because maybe players think they are not then focused on what they have to do. There is no bid for any player, no bid by the club.
“We have to deal about rumours from the press and maybe from Manchester United – I don’t know because there is no contact and no bid for nobody and we don’t sell any more players. That is very clear in my opinion.
“I spoke to Sadio and I will speak to everybody we have to deal with those rumours, we made a statement and everyone knows that statement.
“We will always have rumours, but nobody is for sale. We like to continue with these players and that’s the most important.”
Koeman has seen a host of first-team regulars depart St Mary’s since his appointment last summer, with Morgan Schneiderlin and Nathaniel Clyne leaving this year after Rickie Lambert, Luke Shaw, Adam Lallana, Dejan Lovren and Calum Chambers all departed 12 months ago.
But he is keen to keep hold of Mane, who joined from Red Bull Salzburg last year, and believes Saints are suffering because their players will always be linked with seemingly bigger clubs.
“That is the worst situation for the smaller clubs because no-one talks about the best players of City, United or Chelsea because they are in the best place to be,” he said.
“But teams likes Southampton, they have to deal and that is not easy, that makes rumours and everyone is talking about it. We have to play and that is difficult. If they don’t change the (transfer) window from (closing on) September 1st we will always have these rumours.
“Timing is always bad. Worse maybe one day before we play at home but it is always bad. We keep going, it is still not September 1st and there are still 10 or 11 days more, write all you like and we will see what happens.”