There have been calls for new players to be brought into the side after England lost the Ashes series 5-0 to Australia during the winter.
"It's an exciting time in English cricket in that, for the first time in a long time, there's quite a few places up for grabs," Cook told BBC Essex. "That happens when you lose games of cricket and we lost five pretty heavily.
"Everyone knows there are places up for grabs and good performances in the County Championship over the next few months will push peoples' claims. I don't think you rule anyone out."
England will also face India across all formats this summer.