Kovac won his first six games in all competitions after taking charge on a three-year deal in summer 2018, but has overseen two wins in his last eight Bundesliga matches.
Although Bayern currently trail Bundesliga leaders Borussia Dortmund by nine points, Rummenigge insists the former Eintracht Frankfurt coach is the right man for the job and the right man to take Germany's record champions forward.
Watch: Bayern slipped up against Fortuna Düsseldorf on Matchday 12
"We wish to work together with Niko for a long time," the 63-year-old commented in an interview with the Abendzeitung newspaper. "I hope that he’s not only our coach on Christmas Eve in 2018, but also on Christmas Eve in 2019 and 2020.
"He knows Bayern Munich well. He’s a strong character, in a good way, and he’s someone I like.
"Rummenigge was speaking after Bayern booked their place in the the UEFA Champions League round of 16 with a 5-1 thrashing of Portuguese giants Benfica. After dropping points for the sixth time in this season's Bundesliga three days earlier in the 3-3 home draw with promoted Fortuna Düsseldorf, the Bayern CEO is hopeful the performance will act as the turning point for Kovac and his charges.
"I see a coach fighting, ready to change a few things, which he must do," he said. "Everyone at Bayern is ready to give Niko Kovac this opportunity."
Bayern - fifth in the Bundesliga standings after 12 matches - resume their title defence at Werder Bremen on Saturday. They also face Nuremberg (h), Hannover (a), RB Leipzig (h) and Frankfurt (a), as well as Ajax in the Champions League (a), before the year is out.