Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
West Brom have told Bakary Sako to lower his wage demands if he wants to move to The Hawthorns.
The Reds captain is out of contract at the end of the 2013/2014 campaign and is yet to prolong his stay at Anfield, where he has spent his entire career.
Rodgers says he has spoken with the 32-year-old about an extension but nothing has been decided yet.
Gerrard continues to play a key role for Liverpool, with the midfielder impressing as a second-half substitute in the shock FA Cup fourth-round defeat to League One Oldham on Sunday.
Rodgers is keen to sort out the future of the England captain before the end of the current campaign.
He told the Daily Mirror: "Steven and I have spoken a number of times (about a contract), but as yet I don't believe anything has been done.
"His feeling the last time we spoke was get through this season and see how that goes. His focus is on really helping the group to go forward.
"There's no doubt that between now and the end of this season the contract will be looked at."