The Netherlands striker, who has just one year remaining on his contract, signalled his intention not to renew his deal in a statement on his personal website last week, and has since been linked with the likes of Serie A champions Juventus and Premier League holders Manchester City.
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And, given that the Dutchman could leave on a free transfer at the end of next season, Dein believes that it is vital that the north London outfit resolve the issue quickly.
"He has had such a wonderful season and he's been there eight years. He's the club captain, he means a lot to the club and to the fans," he told reporters."Once a player comes out and says something like that it's normally the prelude to a departure. But no doubt they will do all they can to try and keep him and make sure he sees out his last year.
"All I would hope, for the stability of the club, is whether he stays or whether he goes, it happens quickly. You don't want to see what happened last year when you had Samir Nasri and Cesc Fabregas stringing it out.
"Clubs this week are going back for pre-season training. You want to have a settled squad. I hope that whatever happens with Robin, it happens quickly."