Calvert-Lewin suffered a hamstring injury during Saturday's 1-1 draw at Wolves.
The Toffees will have to win to stay up if Leicester beat West Ham.
Defeat against the Cherries leaves their fate in the hands of both Leicester and Leeds.
Sean Dyche's side are two points above the relegation zone heading into Sunday's final day.
Calvert-Lewin has suffered another injury hit campaign for Everton, making just 17 appearances and scoring just twice.
Read more Premier League
MSP Sports Capital signs exclusivity agreement with Everton owner Farhad Moshiri
Saka commits long-term future to Arsenal and says 'time is on our side'
Dyche will now face the dilemma of who to start up front against Bournemouth and will have to choose between Demarai Gray, Neal Maupay or Ellis Simms.
Reflecting on the draw with Wolves on Saturday Dyche said to evertontv: "The main thing for me is the mentality.
"I can't enhance on that enough. We changed the shape three or four times in the second half [at Wolves] and we're asking a lot of the players to keep changing. They were clear-minded, and they just kept going and going.
"We got what could be a big point, but we've got to reinforce that by going again this week."