The 29-year-old Austrian confirmed the deal was imminent in an interview with Servus TV, though he noted the agreement had not yet been made official.
"It fits well," Laimer said. "We have talked a lot about it in the last hours and days and it is not yet official.
"We will see how quickly and when it happens. But it is definitely on a very good path."
The salary had been the sticking point throughout the discussions. Laimer sought to increase his earnings from between €8m and €9m per season to between €12m and €15m, a level Bayern Munich's hierarchy considered too high. Both sides eventually settled on a figure of just over €10m per season.
The deal keeps one of Bayern's most reliable midfielders in Munich through to the end of the decade, with the Austrian international having established himself as an important part of Vincent Kompany's squad since joining the club.
The compromise on salary is a notable outcome given how far apart the two sides had been publicly reported to be during the negotiation period. Bayern's willingness to move above their initial position and Laimer's acceptance of a figure below his maximum demand reflects the genuine desire on both sides to find a solution.
Laimer's versatility — capable of playing in a number of positions across the midfield — makes him a valuable squad asset under Vincent Kompany, and his retention removes the need to invest in a replacement in the current window. The deal is expected to be confirmed officially in the coming days.