But Koeman will face an immediate struggle to stem a predicted talent drain with the club's England defender John Stones already tipped for a move to Barcelona or Manchester City.
"I like to help everybody and sometimes you have something more, he plays where I played," said Koeman. "There will be good support for the boy. I would like to talk to him personally, ask what his feeling is and make conclusions."
Romelu Lukaku is also believed to be considering his options after he returns from Euro 2016 and Koeman said he will also seek an early meeting with the Belgian striker about his club future.
"Lukaku is a key player, a goalscorer, you don't want to lose your best players," he said. "If I can do something about that, I will."
Koeman said everybody at Everton, who finished 11th this season, was ready "to take the next step" towards making the club more successful.
"It's a big history and it's nice to be part of that, to win and play European cup football and win titles," he said. "Everyone is ready to take the next step and I'm one of them. To be involved in this project for the next couple of years is a big feeling."
Koeman has been joined at the club by his brother Erwin and Jan Kluitenberg
(Reporting by Neil Robinson; Editing by Toby Chopra)
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