Meulensteen took charge of the Premier League strugglers at the weekend following the sacking of Martin Jol.
Despite admitting that fans may need to be patient with the new boss, Coleman believes that the Dutchman will keep the team in the top flight.
"I hope it goes well for him, I'm sure it will," he told Sky Sports News. "It's a great club Fulham, it deserves to be in the Premier League, real fantastic set of supporters, I was there for 10 years myself as a player and manager.
"I hope and pray they get out of the bottom three and I hope Rene will keep them up this year, I think he will and then maybe they can build on that.
"But they need to be a little bit patient with him at the start, they just need to get that first win."
Meulensteen will manage Fulham for the first time tonight when they host Tottenham Hotspur in the league.