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Robben, who turns 35 on January 23, is out of contract in June with Bayern, but has reportedly already been approached by PSV Eindhoven and Inter Milan.
The flying Dutchman is tight lipped over the details of the offers he has received since confirming last month that this will be his final season at Bayern, a decade after joining from Real Madrid in 2009.
"I have received a few offers and have to admit they have made me somewhat proud," Robben said at Bayern's winter training camp in Doha.
"The last few weeks have been quite stressful, especially for my father, who is my agent.
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"However, what I said before the winter break is still valid - my future's still open.
"I don't know when exactly, but at some point I will have to make a decision and I won't wait until the end of the season, because I have family and must plan accordingly."
The injury-prone Robben missed Bayern's final five league games of 2018 with a leg injury, but the right winger has still managed five goals and two assists in 15 matches so far this season in all competitions.
He has enjoyed a golden decade in Munich having scored the winning goal in the 2013 Champions League final at Wembley, giving Bayern their fifth European crown with a 2-1 win over Borussia Dortmund and has so far won seven Bundesliga titles.
Bayern kick off the second half of the season at Hoffenheim on January 18 with the defending champions currently sitting second in the table, six points behind leaders Dortmund.