In an interview with AFP ahead of Bayern's Bundesliga opener against Hertha Berlin on Friday, the 1990 World Cup winner said that Kovac could emulate the achievements of Bayern's most successful coaches and lead the club to Champions League glory.
"I think Kovac could even build an era in the way Ottmar Hitzfeld, Jupp Heynckes and Udo Lattek did at Bayern," Matthaeus, 58, told AFP.
Kovac was under constant pressure in his first year at Bayern last season and faced repeated criticism from inside the dressing room, despite eventually leading the club to the domestic double.
"He won the double in difficult conditions last year. He showed he can fight," said Matthaeus.
"He is a football expert and I think this season will be easier for him."
Matthaeus, who won seven Bundesliga titles with Bayern as a player, said that Kovac has been "left on his own" by players who had "the ear of the club bosses".
He suggested that the Croatian would find it easier now that senior players such as Arjen Robben, Mats Hummels and Franck Ribery had left Munich.
"I think the younger players he has now have the potential, the quality and the mentality that Niko needs to play his kind of football," said Matthaeus.
The 58-year-old said that he believed Bayern still had the quality to compete for the Champions League.
"Bayern have 17 players who are really at the top level, but they cannot afford to suffer lots of injuries as they did last year," he said.
"If any German club is going to win the Champions League, it will be Bayern," he added.
'Other countries have overtaken us'
After they took the title race to the final day of the season in 2018/19, many in Germany believe that this could be Borussia Dortmund's year in the Bundesliga.
The perennial runners-up have strengthened their squad with Thorgan Hazard, Julian Brandt and Hummels, and have stated their intention to end Bayern's seven-year hegemony over the German league.
Yet Matthaeus believes that, despite their lack of movement in the transfer market, Bayern remain favourites for the Bundesliga title.
"Dortmund have invested a lot of money, but for me, they still don't have the quality Bayern have."
"There are more Bayern players who would get into the Dortmund team than vice versa."
Matthaeus admitted that, in general, the Bundesliga now lacked the quality of the English Premier League and the Spanish Liga.
"Other countries have overtaken us, you saw that with the English teams last season and the Spanish teams in the last few years."
"They are the strongest leagues in the world in terms of international success."
Yet the former Germany captain warned the Bundesliga against abolishing the much disputed 50+1 rule, which guarantees majority control for club members at most clubs, in a bid to attract foreign investors.
"In England, the investors have created a two-speed society, where you have the top six and then the rest of the league."
"In the Bundesliga, we still have the feeling that the teams fighting relegation can always frustrate or even beat the teams at the top."