The former Liverpool frontman has been left out of the Welsh side's upcoming World Cup qualifying fixtures against Scotland and Croatia due to hamstring problems.
"Players like Craig don't come along all the time," said Coleman. "We need to know from Craig whether he is staying with us or whether he isn't. If he is not, we have to move forward."
Bellamy, who competed for Team GB at London 2012, has been open about his desire to stay on with Wales.