Forster was expected to battle it out for the number-one spot with fellow shot-stopper Artur Boruc, who is in the final year of his contract.
However, Koeman believes that the England international should have a permanent place in the first team due to Boruc's uncertain future at St Mary's Stadium.
"Everybody knows the situation with Artur Boruc – it's the last season of his contract – so this is a choice about the future," the Dutchman told the club's official website.
"I've already spoken to Artur, and Fraser Forster comes in as the first goalkeeper. Artur has to give real competition, and I expect that because that's the professional way."
Southampton begin the new Premier League season on Sunday when they make the trip to Liverpool.