Sarri was asked by Chelsea TV (h/t Metro) if the striker would be available and offered a positive response on his condition.
"I think so. He had a stomachache and a fever," Sarri said. "But no injury, so I think and I hope he will be available."
Higuain was left out of the Chelsea squad for Thursday's trip to Ukraine to take on Dynamo Kiev in the UEFA Europa League to recover from illness:
Olivier Giroud took his place up front for the Blues and hit a hat-trick in a 5-0 victory that secured an 8-0 aggregate win and a place in the quarter-finals.
The French forward may have played himself into contention for Sunday's match and is a decent alternative to Higuain, according to football writer Daniel Storey:
Higuain arrived at Chelsea on loan from Juventus in the January transfer window and has managed three goals in nine appearances for the Blues so far.
However, he failed to impress last time out in a 1-1 draw against Wolverhampton Wanderers:
Sunday's match is an important game for Chelsea in the race for a top-four finish. A victory would see them move to within a point of Tottenham Hotspur in third place, as Spurs, Arsenal and Manchester United are not in action this weekend.
Everton held Chelsea to a goalless draw at Stamford Bridge in the Premier League in November, so the Blues will need to find a cutting edge that was lacking if they are to defeat the Toffees.
Higuain should go straight back into Sarri's starting XI if he is fully recovered from his illness, although Giroud looks a good option to step in if the Argentinian does not make it after his impressive midweek showing.