The rapid 23-year-old wide man, who netted 10 goals in 32 games for the Saints, has attracted the attention of the Premier League giants, who missed out on former Barcelona winger Pedro having opted to move to Jose Mourinho's Chelsea.
Koeman, however, has denied Southampton will not sell any more players after already saying goodbye to the likes of Nathaniel Clyne and Morgan Schneiderlin - the latter moving to Manè's suitors United.
"We're not selling any more players. Write what you want to about the rumors until 1 September, nobody is going to leave Southampton. The situation is so easy and we have to deal with it," said a defiant Koeman.
"I don't like it as maybe players are thinking they're not fully focused on what they have to do. There's no bid for any player. Not for Sadio Mane, the same goes for Victor Wanyama.
"We have to deal with rumors among the press. There's no bid for any player and no contact from any club," Koeman added.
Here's hoping Koeman's word is as reliable as it has been in the past.