Robben, 34, has achieved hero status at Bayern since moving to the Bundesliga champions from Real Madrid in 2009. He has contributed a staggering 93 goals and 62 assists in 182 Bundesliga outings for the Bavarian giants, playing a central role in six German title wins, four DFB Cup triumphs and the 2012/13 UEFA Champions League success.
Watch: Arjen Robben's top 5 Bayern goals!
He is out of contract in the summer, and Bayern president Uli Hoeness has said a decision on his future will be made “in April or May”, while Robben himself told kicker on Tuesday: “I’m simply focussing now on playing football.”
It has been suggested the former Groningen and PSV Eindhoven man will return to his native country before he retires, but De Boer told BILD that would be a mistake.
“He should end his career with Bayern,” said the former Netherlands international defender, who began his own playing career at Ajax in 1998 but finished it in Qatar 18 years later.
“There’s always that thing about going home at the end of a great career. It can go well, but usually it doesn’t. He doesn’t have to prove anything to anyone any more.”
That raises the prospect of seeing De Boer, who was assistant coach with the Netherlands when Robben helped De Oranje to a runners-up finish at the 2010 FIFA World Cup, joining his compatriot in the Bundesliga.
De Boer has been out of football since his short spell in charge of English Premier League side Crystal Palace ended earlier this season.
He led Ajax to four Eredivisie titles in a six-year tenure at the club where he made his name as a player, and then took over at Italian giants Inter Milan in 2016.
Now, De Boer would love the opportunity of following compatriots such as Bert van Marwijk and Peter Bosz into a job in the German top flight.
“I have already had offers from Bundesliga clubs. But my German isn’t good enough yet and to be able to speak is important,” the former Barcelona and Galatasaray player explained. “The Bundesliga is very interesting. I could imagine working in it.”