Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
The Dutchman has taken the helm at Craven Cottage following the departure of Martin Jol.
Wales manager Coleman believes the appointment of the former Manchester United coach is a good move, but has called for Meulensteen to be given time.
Coleman, whose national assistant Kit Symons is among the coaching staff at the London club, told Sky Sports News: "Fulham are in the bottom three. He's not a magician, Rene - he's an excellent coach and he is a good man.
"It may take him a little bit of time. I think as soon as they get the next win, he will try and build on that.
"I hope it goes well for him. I'm sure it will. 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."