The Australian full-back, 28, has been one of Rovers’ most popular players since joining from St George Illawarra in 2017.
However, they have signed fellow Australian Lachlan Coote from St Helens for next season and the club has confirmed Quinlan will move when his deal expires at the end of the year.
McGuire said: “I think Quinny has been fantastic over these last few weeks.
“It was obviously a tough call for the club to make but I’m sure Quinny will have a big finish and a big say in the season for us.
“Sometimes a club has to make big decisions. I think the biggest thing is everybody loves Quinny. He’s a legend and an absolutely fantastic person to be around.
“When Tony (Smith) and Paul (Lakin) have to make these types of calls it’s tough because you don’t want to let anyone down.
“But I’m sure Quinny will pick up another opportunity somewhere as he’s been such a fantastic player for this club,” he added.
Quinlan is set to feature in Sunday’s home game with Warrington Wolves which has been brought forward from 3.30pm to 1.30pm because of England’s appearance in the Euro 2020 final later that evening.
Warrington, meanwhile, have confirmed the signing of England stand-off George Williams on a three-and-a-half year deal.
The former Wigan Warriors star arrives as a free agent after his controversial release by Canberra Raiders in May.
Williams is set to debut against Leigh Centurions on July 22.
Halifax-born former Leeds and Oldham prop John Fairbank – brother of ex-Great Britain star Karl Fairbank – has died at the age of 55.