Clubs outside England have until September 2 to complete their transfer deals, with Monaco linked with the Gabon international.
Premier League clubs can still sell players, which means the 25-year-old could be set for a move abroad in the coming days.
Lemina is considered a talent, but he has not fit with Hasenhuttl's plans at the Saints.
Hasenhuttl said to reporters: "He's [Lemina] one of the guys [likely to leave]. There are a few options for him and it's especially important that this personality is coming to a clear finish.
"We will have a look what happens but it is an option that he leaves us in this transfer period."