They claim the Gabon international is willing to end his two-year stay on the south coast and admitted he has struggled over the past few months.
Last week, Tuttomercatoweb reported that Atalanta had made an inquiry about taking the 25-year-old on loan with an option to buy.
Although the report suggests The Saints are willing to allow the midfielder to leave, it is believed they want it to be a permanent transfer, with Transfermarkt valuing him at £13.5million.
Lemina said: “If I feel I do not like this project, I can leave. They are giving me the opportunity to be able to go elsewhere.
“We are working on it with my agents, we are not putting ourselves under any pressure. We are waiting truly for the best project, the best offer.”
Ralph Hasenhuttl preferred to play James Ward-Prowse, Pierre-Emile Hojbjerg, and Oriol Romeu as his midfield trio.
However, when comparing the four players using Whoscored.com, Lemina was not the worst. He has 1.2 shots per game while Romeu has 0.3. He also beat the Spaniard for key passes per game, assists, pass success percentage and interceptions per game.
Lemina made 21 league appearances last season for the club and could feel this summer may be the right time to move on for more first-team opportunities.