Saints are working hard on a number of deals as they try to hand boss Nathan Jones the tools to take the side out of trouble in the Premier League.
Keane is one of the players Everton are prepared to let leave on loan and it has been suggested Southampton are now looking at a swoop.
The two clubs have not engaged in direct negotiations so far and it is suggested that Everton would not be keen on loaning him to direct relegation rivals.
However, Saints could potentially sign Keane on a permanent deal.
Southampton want to strengthen the spine of the team and view centre-back Keane as possibly a good addition.
Selling could suit Everton as Keane is down the pecking order of defenders at Goodison Park.
And boss Frank Lampard could then put the cash into his own transfer kitty as he looks to make new signings this month.
