Manchester United striker Berbatov quit the national team in May citing personal reasons, with many linking Bulgaria's weak start to the European Championship qualifying to his absence.
Matthaus, who succeeds Stanimir Stoilov as coach, is hoping the 29-year-old will return as he looks to revive the squad.
"I plan to start talks with Berbatov," said Matthaus.
"He is still welcome in the Bulgarian national team. As a Bulgarian player he should be proud to play for his country."
Former Germany midfielder Matthaus has revealed his number one objective is qualification for Euro 2012.
"I am going to try to catch up on what has been lost," he added. "We want to finish at least second in our (Euro 2012 qualifying) group."
Matthaus, 49, penned a one-year contract with the national team on Thursday with the option for two more years.