"We have to put an end to this mess," Bulgarian Football Union (BFU) vice-president Yordan Lechkov told local media on Sunday.
"Lubo Penev must be the national team's coach in the next four years. And he shouldn't be touched during this period."
Former Valencia and Atletico Madrid striker Penev led Litex Lovech to the domestic league title last season with his team also among the favorites this season.
The pressure on the 50-year-old Matthaus, who captained West Germany to success at the 1990 World Cup and won a record 150 caps, has increased following Bulgaria's recent defeats in the Euro 2012 qualifying.
The Balkan side lost at home to Group G leaders England 3-0 and then were beaten 3-1 by Switzerland.
Those results left Bulgaria fourth in the standings with five points from seven games and out of the running for the finals.
Matthaus, who became the first foreigner to coach Bulgaria since 1966 last September, achieved limited success as a coach with Rapid Vienna, Partizan Belgrade, Brazilian side Atletico Paranaense, Salzburg, Israeli club Maccabi Netanya and Hungary.
Bulgarian Prime Minister Boiko Borisov, who plays for a third division team, also criticised Matthaus.
"Vitosha Bistritsa [Borisov's team] defend better than Bulgaria," said the prime minister after an exhibition match earlier this week.
"He [Matthaus] wouldn't be bored here, there are some very beautiful cheerleaders," Borisov added sarcastically.
In February, Matthaus officially put an end to his fourth marriage as he already announced two more relationships since.
