The 28-year-old has two years left on his current contract, but he needs to stay fit to stand a chance of earning a new one.
Otherwise West Ham may cut their losses on their one-time record signing next summer, rather than risk him leaving for nothing 12 months later.
Carroll, who cost £15million from Liverpool, has missed 114 matches through a catalogue of injuries since he signed for the Hammers in 2012.
He is currently fit, however, and poised to lead the line in Saturday's lunchtime London derby against Tottenham.
Manager Slaven Bilic said: "He's got two years and this is, to be fair, his season to be fit, to stay fit.