Gibson doubtful for Chelsea clash
The Ireland midfielder, 25, was substituted at halftime in Everton's midweek win over Wigan Athletic.
"He has got a bit of a thigh strain... we will assess him and see how he is," manager David Moyes told reporters.
Everton currently sit fifth in the table after a solid first half of the season and would leapfrog their opponents on Sunday were they to win.
Right-back Seamus Coleman could return to action after missing the last two matches, Moyes said.
Marouane Fellaini will not play as he is serving the final game of a three-match ban.