Hammers co-owner David Gold was recently quoted as saying that he sees Rice as a future England international, despite the defender having won one cap for Ireland.
Rice is entitled to switch national teams since he has not made a competitive appearance for either, but Keane was quick to dismiss Gold's comments.
"It's going to be pretty difficult if he's Irish, and he is Irish, he plays for Ireland," the Evening Standard quotes the former Manchester United midfielder as saying.
"Where else would he want to go? If you had a choice, Ireland or England... It's pretty straightforward. Ireland."
Reports suggest that the England setup is indeed monitoring Rice's progress.