The Dutch winger scored a hat-trick for Bayern against Hertha Berlin on Saturday and has attracted interest from Chelsea as well as Manchester City.
His father and agent has confirmed he has received interest from the two English clubs and with only one year left on his contract, he could leave for as little as £10m in the summer.
According to the Daily Mail, Bayern president Karl-Heinz Rummenigge has offered Robben a £170,000-a-week contract, which would see him become the highest paid player in their history.
Rummenigge said: 'Arjen can make all the difference in a team. That's why I want him to stay.'