Bayern president Karl-Heinz Rummenigge, in an interview set to appear in the German press on Thursday, said the two sides had resolved their differences over Robben after the winger returned from the World Cup with an injured thigh.
"The Dutch want to resolve the situation," Rummenigge told German daily Munchner Merkur.
"We've suffered sporting and financial damage. The solution is a match between the Netherlands and Bayern which will enable us to cover our losses. The two sides are in agreement with this solution."
The deal brings to an end a saga that has been simmering since August with Bayern threatening to take the KNVB to court over Robben, who was only able to resume full training last week.
He is set to have his first league run out of the season against Wolfsburg on January 15.