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.
Jurgen Klopp was left encouraged by Germany's performance in his first match as head coach, despite seeing his side concede a late equaliser in a 1-1 draw with the Netherlands in the UEFA Nations League on Thursday.
Dani Olmo's agent has welcomed reports of interest from Bayern Munich, but the Barcelona midfielder remains focused on fighting for his place at the Catalan club.
Cody Gakpo struck in the 92nd minute to deny Jurgen Klopp a winning start as Germany head coach, with the Netherlands rescuing a 1-1 draw in Amsterdam.
Moussa Diaby believes he still has plenty more to give after making his return to Bayer Leverkusen this season.
