Brendan Rodgers has confirmed he will offer Steven Gerrard a new contract at Liverpool as the club close in on the £12m signing of Daniel Sturridge from Chelsea.

Liverpool's attempts to sign Sturridge early in the forthcoming transfer window hit a complication after the 23-year-old's representatives demanded a percentage of any future sell-on fee. The club's refusal led to a medical being postponed on Merseyside on Wednesday but following further talks between the managing director Ian Ayre and Octogan, the medical was re-booked and took place on Sunday.

No deal can be officially announced until 1 January but with Sturridge having agreed personal terms prior to the hitch with the agents, and the fee agreed, a significant obstacle in the way of the striker joining Liverpool has been overcome.

Rodgers is also keen to secure the pillars of Liverpool on long-term contracts and has revealed Gerrard's contract at Anfield – which expires at the end of the 2013-14 season – will not be the captain's last with his boyhood club.

The Liverpool manager said: "Steven is vital to us and I recognise that. I know he has 18 months left on his contract but I would want him to go beyond that for this club and this team. What I would say with Steven is he has a real hunger to succeed. He may be 32 years of age, but he's still got so much left. He applies himself right, he eats well, he recovers well, he works well, he does everything right.

"This is a guy who has led his life right as a football player and that allows you to play well into your 30s. I would want him to stay beyond his current contract and extend it. There is absolutely no question about that. He has played every minute of every league game for us which shows what an incredible figure for us he is."

Gerrard scored for the second week in succession at Anfield as Liverpool cruised to a 4-0 win over Fulham on Saturday, having gone 17 games without a goal for club and country before the consolation against Aston Villa. The England captain has come under scrutiny for his lack of goals and altered role under Rodgers this season but the manager insists the influence remains as great as ever.

Rodgers said: "You look at his stats this season and he is right up there as one of the most influential midfielders in the Premier League. He's at the top in chances created, passing, possession; all the important things. I find it incredible he can have had any criticism at all. It is absolutely ridiculous. From seeing him every day working, and seeing him playing in the games, it's incredible.

"OK, he may not be getting the goals he did five or six years ago but that doesn't stop you influencing the game, and his influence for me – and especially once he was starting to understand what I'm looking for – has been absolutely top class. He has been an inspirational captain for us, he has been a huge figure in the development of this team. We are improving, we are growing, and he has influenced that."