Hart is expected to play in every one of the Three Lions matches at Euro 2016, but the Manchester City stopper is under some pressure after making an error in Roy Hodgson’s side’s last match against Wales.
Hart failed to stop a Gareth Bale free-kick, and Koeman has suggested that Forster has the capabilities to step-in, should the former Shrewsbury man continue to make mistakes.
“Having worked with Fraser Forster at Southampton I know how good he is,” Koeman said.
“Hart is still England’s No.1. But without any doubt Forster could step up and be Hart’s successor. I’m absolutely certain of that.”
Koeman completed a move from Southampton to Everton last week, and Forster could yet join him at Goodison Park.
Everton are known to be on the look out for a goalkeeper, and the Liverpool Echo suggest that Koeman is interested in bringing Forster to Merseyside.
Forster would be an expensive addition for Everton, but Koeman does have over £100 million to spend so he would be able to afford the England international.
It was initially suggested that Koeman would not be able to sign any players from Southampton for Everton, but it seems that those reports have been wide of the mark.
Everton currently have Joel Robles as their number one choice, but the Spaniard is expected to only be retained as a covering option next term.