Speaking during Bayern's traditional Oktoberfest visit, Hainer told BILD that the Bundesliga champions want to prolong their relationship with the England captain and believes a renewal will ultimately be secured. Kane's current contract runs until the end of the 2026/27 season.
"We want to extend with him and I also think that's what will happen,” Hainer said, as quoted by BILD.
The 33-year-old has also offered an encouraging update, describing the situation as "looking pretty good".
However, there is still work to do, with the duration of a new agreement among the principal issues under discussion. Deals running until 2029 or 2030 have reportedly been considered.
Hainer pointed to Kane and his family being settled in Munich as another reason for optimism, while Bayern CEO Jan-Christian Dreesen has suggested negotiations could reach a conclusion after the next three-week international break.
Kane's case for an extended stay has been strengthened by his remarkable goalscoring record. He struck 73 competitive goals last season and remains prominent in the Ballon d'Or conversation.
Harry Kane has revealed he still has huge respect for Jose Mourinho and believes the Portuguese coach can make Real Madrid an even tougher opponent for Bayern Munich in the Champions League.
Maximilian Beier has responded to his omission from Germany's latest squad by scoring the goal that kept Borussia Dortmund's perfect Bundesliga start intact on Sunday.
Bayer Leverkusen produced a strong defensive display and made the most of their chances to beat RB Leipzig 2-0 at the BayArena on Sunday.
Borussia Dortmund defeated VfB Stuttgart 1-0 at the MHP Arena to go the summit of the Bundesliga table in an action-packed Saturday in the German league.
