With his deal set to expire at the end of next season, Lewandowski's future has been the subject of much speculation.
It was reported this week that Bayern were open to selling the Poland captain at the end of the season to avoid losing him on a free transfer.
Lewandowski on Monday won The Best FIFA Men's Player award for the second straight year, having scored an astounding 82 goals in 68 games in all competitions for Bayern since the start of last season.
That is the most of any player from the top five European leagues. Erling Haaland is his closest rival with 64 strikes in 61 appearances for Borussia Dortmund.
Hainer remains keen for Lewandowski to extend his stay at the Allianz Arena, though he insists there is no rush for an agreement to be reached.
"I've already said this a few times. I would be happy if Robert ended his career at Bayern," Hainer said.
"Our sporting management is in constant contact with the players. We still have a little time with him. The contract runs until 2023."
Hainer suggested a new contract for goalkeeper Manuel Neuer, reportedly until June 2025, is much closer to being confirmed. The Germany star's existing deal is also due to expire at the end of next season.
"I am absolutely convinced Manuel will end his career at Bayern Munich. He can certainly play at this level for a few more years," said Hainer.
"He's still the world's best goalkeeper for me, and I'd be happy if we can announce it at some point.
"We are in no hurry. Manuel knows what he has in us. We know what we have in him. He's been with us long enough now, so there is no rush. But at some point, I hope, it will happen."
Defender Niklas Sule is only under contract until the end of this campaign and he has been linked with Barcelona and a number of Premier League clubs.
Hainer confirmed an extension has been offered to Sule and he has a deadline to make his decision so the club are not left scrambling for a replacement.
"We made Niklas an offer. Now it's up to him to accept or reject that," said Hainer.
"Of course, it has to be within a certain period of time because we have to position ourselves accordingly.
"I don't know the exact date right now, but it will certainly be at some point in the foreseeable future that he will say what his wishes are. Then we will take to him."