Robben's contract with the German Bundesliga giant expires in the summer of 2013 and the 28-year-old's future at the club had been the subject of transfer speculation.
However, the Bild reports that the former Chelsea winger is ready to put pen to paper on a new deal although it is understood this will only happen at the end of April.
Robben endured a difficult start to the current campaign with injuries stopping the Dutchman from being able to add any sort of consistency to his game. This has not been the case in the second half of the season where Robben has been excellent including playing a starring role in Bayern's 2-0 win over Marseille at the Stade Velodrome in a midweek UEFA Champions League first leg quarter-final clash.
On Saturday, a Robben goal in the 69th minute decided the Bavarian derby in favour of Bayern as they beat Nuremberg 1-0 to move to within three points of Borussia Dortmund at the Bundesliga summit.
Bild claim the Dutchman will add two more years to his contract.