Chelsea have had two bids rejected so far in the transfer window, their latest close to £30 million, and Red Devils boss David Moyes has stated his intent to keep hold of the forward, who has his heart set on a departure.
"For both sides it would be better if it was to be sorted out one way or another," Crouch told Sky Sports News.
|6/5||Wayne Rooney is 6/5 with Paddy Power to leave Manchester United this summer
"As soon as he arrived at United he hit the ground running and scored loads of goals - he is a very important player."
Crouch did not receive a call-up alongside Rooney for England's friendly match against Scotland at Wembley on Wednesday but, despite not playing since Roy Hodgson took over as manager, he retains hope that he could still play for the Three Lions.
"There have been a few squads since the new manager took over and I haven't been involved," the Potters forward added. "It doesn't bother me too much.
"Obviously I have played a few times for my country and I absolutely loved it but first and foremost is to do well for your club. That's what I've got to do and, if the call came, then great. If not, so be it, it's certainly doesn't bother me too much."