By PHIL THOMAS
The Geordie yesterday withdrew from England games with the Republic of Ireland and Brazil due to a heel injury.
The Hammers hope the lure of regular first-team football in a World Cup year will persuade the 24-year-old forward to move from Anfield.
West Ham’s bid is an initial £12m plus an additional performance-related £4m.
It is now down to the player, who said of his loan spell at Upton Park this season: “I have enjoyed every minute.
“I have just tried to play my best in every match, score goals and keep myself fit.
“I have had a great season. This is a great club.”
Carroll cost Liverpool £35m from Newcastle in the wake of Fernando Torres’ £50m transfer to Chelsea but has failed to make an impact at Anfield.
And West Ham sources insist he is “giving serious thought” to a permanent move to East London.
Carroll’s injury is a major blow to England boss Roy Hodgson, who wanted a good look at the 6ft 3in striker with a view to the crucial World Cup qualifiers in September and October.
Hodgson said: “He gives another dimension to our squad.
“There’s always room for a centre-forward who is good at holding the ball up and attacking crosses.”