The 20-year-old's future is the subject of much debate amid links with Manchester City, Manchester United, Real Madrid and Chelsea, but Matthaus believes that Bayern is a realistic destination for the forward as they prepare for life without Lewandowski.
Speaking to Sport 1, the 59-year-old said: "Haaland is already on the list of top clubs, right at the top as a striker. At Real Madrid, because with Karim Benzema they have a player of a certain age. His father has already played in the Premier League. That could be interesting too.
"He will not serve Borussia Dortmund for life. He'll look for bigger clubs, he'll get a higher income. If he stays in the Bundesliga, there is only one step for him: FC Bayern.
"He could succeed Robert Lewandowski at Bayern Munich in two or three years if Lewandowski should think about the end of his career,' said the former Germany captain.
"But, Lewandowski is currently in form, Haaland too and as long as Lewandowski is playing for Bayern, I don't think Haaland will come, because they will not be able to play with a Haaland-Lewandowski double because they would take away each other's strengths.
'Bayern will not think about selling Lewandowski. He will end his great career in Munich. Only when Lewandowski is no longer with Bayern will the place for Haaland in Munich be freed up."