The Mirror says Carroll has told West Ham he is unable to train.
Carroll claims he has an ankle injury, but scans taken by the Hammers are understood not to show a problem.
The forward has missed West Ham's last three games, including Tuesday night's FA Cup replay win over Shrewsbury.
The Irons have yet to receive a formal bid - loan or otherwise - for the 29-year-old striker from Chelsea.
However, West Ham are aware that Chelsea want a loan move for their target man, who has 18-months left to run on his £100,000-a-week deal. The Hammers would prefer a permanent deal and would be interested only in offers over £20million for their player.