Lookman worked with Saints boss Ralph Hasenhuttl during his time on loan at RB Leipzig during the second half of last season, and the Austrian coach is keen to reunite with the England Under-21 international.
Everton rejected a series of bids - the last of which totalled £22 million ($28.1m) - during the summer transfer window from Leipzig for Lookman, with the Toffees holding out for a fee closer to £27m ($34.6m).
Despite that, Lookman has struggled to hold down a place in the Everton first team under Marco Silva, with the Portuguese preferring the likes of Richarlison, Bernard and Theo Walcott in wide positions.
Saturday's FA Cup third round win over Lincoln City marked just Lookman's third start of the campaign, with the 21-year-old finding the net against the League Two leaders.
Silva has previously spoken of his admiration for the ex-Charlton Athletic trainee, and hinted that more first team opportunities may arise during the second half of the season.
“I never had any doubts about that [Lookman’s ability],” Silva told EvertonTV . “From the first day I came in and started to work with our squad, I didn’t have any doubts about his quality, what he can achieve and what he can do playing in our shirt.
“It is up to us to work with him and give him all the conditions to grow. But I don’t doubt he will be an important player for us. He is already – but he will become more and more so in the future.”
Despite that, Hasenhuttl is hopeful that his previous relationship with the player could tempt Lookman to move to the south coast and attempt to help the Saints steer clear of the relegation zone.
Any move, however, may have to wait until the end of the window, with Southampton hopeful a loan move can be negotiated if it becomes clear over the next few weeks that Lookman is set to remain on the periphery at Goodison Park.
Since arriving at St. Mary's Stadium as a replacement for Mark Hughes, Hasenhuttl has overseen an upturn in form for the Saints.
Victories over Arsenal and Huddersfield Town as well as a goalless draw away at Chelsea have boosted their hopes of survival, though they remain in the bottom three ahead of Saturday's trip to Leicester City.