The prolific striker was crowned Germany’s Footballer of the Year for 2021 last week after scoring 41 Bundesliga goals to break Gerd Muller's long-standing single-season record.
His 48 goals in all competitions were the most scored by any player in Europe's top five league in 2020-21, followed by Kylian Mbappe (42) and Erling Haaland (41).
Lewandowski has netted 294 goals in 329 appearances overall for Bayern since joining from domestic rivals Borussia Dortmund in 2014, including 203 in 219 league games.
But the 32-year-old has been linked with a move away from the Allianz Arena this transfer window, with Real Madrid, Chelsea and Manchester City all reportedly interested in striking a deal.
However, new boss Julian Nagelsmann recently said he is not bothered by the speculation and president Hainer has reiterated Lewandowski is going nowhere while under contract until 2023.
"Firstly, in my opinion, Lewandowski is the best striker in the world. We are so happy that we have him in our team," he said.
"He still has two more years on his contract. He will definitely play those with Bayern Munch. I said it already a few weeks ago – I could imagine him staying with us for even longer.
"He will honour his contract. He will definitely play the next two seasons here at Bayern Munich."
Borussia Dortmund striker Erling Haaland has previously been touted as a possible replacement for Lewandowski, but Bayern are not currently in the market for a new striker.
"As I said, Robert will definitely be here for the next two seasons with Bayern. Then we will look for a successor," Hainer said.
Joshua Kimmich is another valuable Bayern player who has two years to run on his existing deal, while Manchester United-linked Leon Goretzka is set to become a free agent at the end of 2021-22.
Both players returned to training this week after being given an extended break following their Euro 2020 exertions and talks over fresh terms will soon commence.
"As you know, they went on holiday after the European Championship," Hainer said. "They were back yesterday in the training sessions.
"Now we have time to talk to them. And hopefully, within the next week, we will find agreements with them.
Nagelsmann's men then face Napoli before beginning their 2021-22 campaign with a DFB-Pokal tie against lower-league opposition Bremer SV on August 6.