The Saints want to do business before the transfer window closes and have zeroed in on Everton winger Walcott as an option.
However, with the clock ticking down on the transfer window, Southampton do not yet have an agreement with Everton in place.
They want to sign Walcott on a loan deal and the winger faces the prospect of reduced playing time if he stays at Everton, with Carlo Ancelotti having made a number of additions.
Walcott has so far clocked just 12 minutes of football in the Premier League for Everton, across four games.
He was handed an outing in the EFL Cup, but could be attracted by the idea of a move to former club Southampton.
Walcott made 22 appearances for Southampton during his time on the south coast, scoring five goals, before leaving for Arsenal in 2006.
He made the move to Everton in 2018 and it remains to be seen whether he will return to Southampton today.
