The Senegal international joined Southampton from Red Bull Salzburg in 2014 and enjoyed an impressive debut campaign, firing home 10 goals in 30 Premier League appearances.
Mane has continued his good form this season, scoring six goals in 17 games for the south-coast club as the Saints look to improve on their current position of eighth in the table.
The winger was believed to be a late transfer target for the Red Devils during the summer, as covered by the Mirror, but a big-money move failed to materialise as Louis van Gaal instead wrapped up a deal for Monaco’s Anthony Martial.
Chelsea are also said to be interested following their abysmal start to their title defence, but Saints boss Koeman is adamant that nobody, including Mane, will leave the club in January.
He said: “You can ask every week about Sadio going to United or Chelsea, but we will sell nobody in January.
“The team and the club is growing. We have 17 or 18 international players and they are showing the qualities needed in the Premier League so the big teams are obviously showing interest.
“It is normal for players to want to play at the highest level but we are not selling.”