Cork, who joined from Chelsea, made 33 appearances in all competitions last season as Southampton secured an impressive eighth-placed Premier League finish, although Crystal Palace, Swansea and Fulham have all been linked with a move this summer.
Fonte, meanwhile, featured 38 times for the Saints during the previous campaign and his future has also been the subject of much speculation this summer, with Cardiff reported to have had a bid rejected and Hull City also said to have shown an interest.
Koeman only replaced Mauricio Pochettino in charge of Southampton last month and he plans to assess the futures of Fonte and Cork in the coming weeks.
"It's a little bit too fast to have that kind of opinion. I need more time," he told the Daily Echo.
"But they are important players and, as always, if they will come in the last season of a contract, you have to do something at the club, and we will talk about that and we will make decisions about that.
"But it's a little bit too early now."