Nick Compton and Joe Root are believed to be the players in contention to replace Andrew Strauss as Cook's opening partner. However, England could decide to promote Jonathan Trott or Ian Bell up the order.
"This game and the next game we will decide," said Cook. "It's a cut-throat business. You're trying to pick the best player to do it, and they've both got an opportunity to score runs and push their claim.
"So that's what it is. I think they both know the situation."
Cook will be rested while Compton and Root open the batting in the tour match against Mumbai 'A', beginning on Saturday.