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."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!