Talks are expected once the striker returns from a break in the United States.
"Both parties are very keen [to extend his contract]," Dreesen told reporters. "Now we need to make sure those expectations align and that we find common ground.
"As far as I know, he is still in the USA. We will speak when he returns, as we had arranged."
Sport Bild has reported that Bayern Munich's target is a deal running through to 2029, with sporting director Max Eberl expected to join Dreesen in leading the negotiations.
Kane's current deal expires at the end of the coming season, and Barcelona have previously been credited with interest, though Bayern have been consistent in stating they want to keep him.
The 33-year-old, who joined from Tottenham in the summer of 2023, scored 61 goals and provided seven assists in 51 appearances in all competitions last season as Bayern won the Bundesliga by a 16-point margin over second-placed Dortmund; his Bundesliga-specific tally stood at 36 goals and five assists from 31 league appearances, 25 of them starts.
He has scored 146 goals in 147 appearances for Bayern in total, becoming the fastest player to reach 97 Bundesliga goals, doing so in just 94 matches, and the first player in league history to finish as the division's top scorer in each of his first three seasons.
Kane capped his club season with a third-place finish for England at the World Cup this summer. Dreesen also used the press event to dismiss speculation over Michael Olise and Luis Diaz, both of whom have been linked with moves away, saying no contact had been made by interested clubs over either player. Olise had been strongly linked with Real Madrid after being named Bundesliga Player of the Season and setting up seven goals for France at the World Cup, while Diaz enjoyed an impressive debut campaign in Bavaria following his move from Liverpool.
"We'd be foolish to [sell them]," Dreesen said of Olise and Diaz. "We have such a good team. Let them play and score goals." The comments underline Bayern's determination to keep their attacking core intact as they prepare to defend their Bundesliga title, with Kane's situation regarded as the priority given the shorter time frame on his contract.