Schneiderlin has been one of Mauricio Pochettino’s key men for Saints, who recently admitted a summer move to a top club would be hard to turn his back on.
He revealed: “For my progress and my visibility, it would be better to play for a club who play in the Champions League.
“I know there is a lot of speculation, but I still have three years on my contract, it does not depend on me.
“We’ll see in the coming weeks.”
Brendan Rodgers has reportedly already open talks with Southampton over the sale of centre-back Lovren and is also interested in signing England international Adam Lallana.
Rodgers is keen to strengthen Liverpool’s slim squad as they look to take on the extra pressure of competing in the Champions League next term.