The Sun says the Hammers are desperate to sign the on-loan striker permanently but cannot afford the £17m asking price because of tough incoming financial rules.
Carroll, who cost the Reds £35m in 2011, is also paid more than £80,000 a week.
And that has put a huge strain on the debt-ridden club's bank balance as the Premier League prepare to impose spending controls from next season.
An Upton Park insider said: "Under the new rules the wage bill will be capped at just over £45m. Andy's on £4m a year. If you break the rules there are points deductions.
"The only way West Ham could do a deal with Liverpool is by juggling the fee because he shouldn't have to take a wage cut. That means very few clubs can afford him.
"Everyone has to live within their means from next season onwards.
"He's doing well here now after injury problems and the people upstairs are desperate to try to work something out by juggling the figures.
"Whether it is Andy or not, we need two top-class strikers and four or five new players in the summer."