The 29-year-old forward, who is due to miss West Ham's FA Cup third-round replay against Shrewsbury tonight through injury, has been linked with a temporary move to Chelsea.
Boss Antonio Conte is keen to bolster his attacking options after seeing his side go three successive matches without scoring a goal, and there has been talk of a loan deal for the remainder of the season.
However, Hammers assistant boss Alan Irvine believes loaning Carroll, who has scored just twice during another injury-hit campaign, is out of the question.
"I certainly hope Andy will be a player here at the end of the month," Irvine said. "I don't think we have had any offers, in terms of taking him on loan, and I don't think the club would entertain him going out on loan.
"That does not help us and we need as much help as we can get between now and the end of the season, so I don't know why that would be attractive to the club if it was to come up.
"There has been a lot of talk about it, but not necessarily anybody doing anything about it."