England need a win in the Test starting Friday in Ranchi after successive losses put them 2-1 down in the five-match series.
The all-rounder Stokes previously said he would play purely as a batsman in the series because of his knee, but bowled in the nets on Wednesday.
He has struggled with his left knee for some time, stopping him bowling in the last three Ashes Tests in 2023 and the ODI World Cup.
"There's definitely a chance," vice-captain Pope said of the probability that Stokes will bowl in the fourth Test.
"He's not confirmed it even in the changing room so we will see. He bowled at the batters today," he added.
"See how he pulls up, and if that's good, hopefully we will see him with the ball in hand in the game."
Stokes underwent knee surgery in November and has been working his way back towards full fitness.
"If he's got full confidence in his knee I guess you've got to trust the medical advice and trust his opinions as well," added Pope.
Stokes is a right-arm fast bowler who completed 100 Tests in England's 434-run loss to India in the previous match.
He is on 197 wickets, three short of becoming only the third man in five-day cricket with a double of 6,000 runs and 200 wickets.
England are expected to rest pace bowlers James Anderson and Mark Wood for the match on a Ranchi pitch expected to help the spinners.
