Martinez has been playing with a sore right ankle, an injury he suffered in Game 1. Martinez looked hobbled when running during Game 2.
Cora said Thursday that Martinez's ankle is feeling better and that he will continue to get treatment ahead of Game 3 before the team makes a decision.
"We'll see," Cora said of Martinez's status.
Later Thursday, Cora seemed more hopeful when he spoke to ESPN's Enrique Rojas.
"He should play," Cora said. "We don't know whether he will play left or right field, but that decision as to where we will make overnight or during the day tomorrow. First we have to see if his ankle feels good. Yesterday at the beginning of the game he was hobbling a bit, but then he felt good. I hope that tomorrow morning he feels much closer to 100 percent."
Martinez said he feels optimistic about taking the field.
"Right now I plan on playing," he said. "I feel like it's going to be fine."
Cora had previously said Martinez would shift from his usual designated hitter spot to right field for all World Series games at Dodger Stadium -- a move that would likely force Boston to bench either Jackie Bradley Jr. or Andrew Benintendi.
Cora also said Thursday that Mookie Betts will not start at second base in Game 3.
"No, he's not playing second base [on Friday]," Cora said. "I mean, he's not starting at second base."