Calvert-Lewin picked up a hamstring injury in Everton’s 1-1 draw at Wolves last weekend and hobbled off the pitch.
Everton have been closely monitoring the injury and have been hoping that he regains fitness enough to be in the squad against Bournemouth.
But it has been claimed that the growing expectation is that the striker will not be fit to face the Cherries at home on Sunday.
The medical team have been keeping tabs on his recovery but the club are now worried that he will not be fit.
A win at home on Sunday would guarantee Everton Premier League survival but a draw would force them to depend on other results to avoid getting relegated.
Calvert-Lewin has performed well in recent games, scoring in the crucial draw against Leicester and playing brilliantly in the 5-1 win over Brighton.
But with him unlikely to be fit, Sean Dyche will have to choose between Neil Maupay and Ellis Simms for the number 9 role against Bournemouth.
