The offer could see Carroll move to Upton Park on-loan for a season with the move becoming permanent the following summer.
His former club Newcastle have also shown an interest in bringing the striker, who was sold by the club for £35million 18 months ago, back to St. James's Park.
New Liverpool boss Brendan Rodgers is open to offers for the young striker, saying:
"Andy is a terrific young player," Rodgers said. "I had a brief chat with all the lads and over the next couple of weeks I'll be able to speak to them with more confidence and on a one-to-one basis.
"There is no doubt he is a terrific talent. There has been a lot of unfair criticism aimed towards Andy. He is a player who can play in a number of styles and it was a wee bit unfair on him to say he couldn't fit into the way I would want to play.
"We've got a number of very, very talented players in the group, of which Andy is one."