The 33-year-old started his career with the Eredivisie side and holds close ties to them, with the prospect of a return being raised by Hans Nijland
Groningen director Hans Nijland says it would be an "absolute dream" if Arjen Robben were to return to his previous side.
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The Bayern Munich attacker rose through Groningen's youth system to star for the first-team at 16, before moving on to PSV, Chelsea and Real Madrid.
Robben, 33, has always maintained a close relationship with his hometown team, though, and the possibility of ending his career there has often been suggested by both sides.
Nijland has no doubts the move would be good for the club, just as Dirk Kuyt's return to Feyenoord led them to a first Eredivisie title in 18 years this season.
"He played here from the age of 11 and made his first steps on the field here," he told RTV Noord. "He even also opened our stadium.
"Arjen keeps warm ties with us and vice versa. Obviously, we've talked tons about him returning. We've seen it now with Dirk Kuyt and Feyenoord.
"It would be an absolute dream. If Arjen would be willing to return, he is more than welcome. If someone like Robben can add to your club, then you must take the next step.
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"There is a beginning and an end somewhere in his career. We'd all love it if he were to do something for the club."
Robben scored 15 goals in 36 appearances in all competitions as Bayern won the Bundesliga and reached the Champions League quarter-finals, losing to Real Madrid.
He is contracted to the Bavarian side until June 2018.
- Goal