The Saints understand the player wants to move on, but they would prefer a direct sale if a move is to happen.
Reports in Italy indicated that Atalanta would make a loan offer.
The Daily Echo says no formal offer for Lemina has arrived.
The Gabonese international will stay with Southampton unless a permanent transfer offer in the range of what the club paid to sign him arrives.
Lemina arrived in 2017 for £15 million.