Carroll, the forward, went under the knife to cure a long-standing ankle problem which flared up again last month.
The 30-year-old was a doubt to be back in time for the end of the campaign even without choosing the surgery route, but the Daily Mail report there is now no chance he will play again this season.
And this means Carroll will not add to his 142 West Ham appearances, with the east London club not planning on offering him a new contract when his existing deal expires this summer.
Carroll, who first joined West Ham on loan from Liverpool seven years ago, has endured an injury-hit spell with the Hammers.