The Brazilian appears to be pretty low down the pecking order at the moment having missed out on the first team squad entirely for the Reds' opening day victory over Stoke City at the Britannia Stadium.
Now it appears that Liverpool are open to offers of around £8 million, with the Daily Mail reporting that two clubs from Italy are interested in signing the 28-year-old.
But Molby argues for the Reds to keep hold of Lucas, even if his first team opportunities may be limited, saying: "I really hope he stays because I still think he will have a part to play this season. It’s important you have a No.6 who is a proper No.6 and very much a team player – someone whose ambition is for the team rather than himself.
"I’ve always liked Lucas. You have to have admiration for the way in which he has stuck at it. He believed he was good enough to succeed at Liverpool and he’s proved that was the case.
"I think there will be games where you need Lucas. I don’t see Emre Can playing that holding role. I don’t think he has the mindset or the discipline for it as he will feel he has more to offer further up the pitch."
Some would agree with the view that Molby offers but Emre Can seemed to impress during his spell in the defensive role when he came on as a substitute during the win at Stoke, but it is thought that Lucas is the only natural in that position while the German is more versatile and can play further forward as well as across the back line as demonstrated last season.
There will be times when Liverpool will require someone to anchor the midfield at times this season, and Rodgers feels Emre Can is the man to do it, but the experience Lucas has playing in that role could be handy, and losing him means losing a pretty influential and experienced figure in the side.