Low announced on Tuesday he will step down from his role with the national team after the Euro 2020 finals, having been in charge for the past 15 years.
Bayern Munich's Flick was installed as one of the early favorites to take over from Low, whom he previously worked alongside as assistant head coach for eight years.
The 56-year-old appeared to rule himself out of the running earlier this week as he remains under contract at the Allianz Arena until 2023.
But Bayern CEO Karl-Heinz Rummenigge will leave his role at the end of the year and Matthaus has urged the DFB to move for Flick should he become available.
"He's a person of harmony, but he has to feel good," Matthaus told Sky Sport Germany. "If he no longer feels comfortable at Bayern, he will tell his bosses and then he will be the ideal candidate for the national team."
Meanwhile, Matthaus previously stated he had no interest in leading the country he represented 150 times as a player, but he has now changed his stance.
"The DFB has to think about what it wants. Pros and cons are weighed up against each candidate," he said.
"I'm someone who likes to help. If I had the feeling that those responsible were united behind the decision, I would start to think about it."
Germany Under-21s coach Stefan Kuntz and former Leipzig boss Ralf Rangnick have also been linked with the position, though the latter is reported to be in talks with Schalke over the possibility of returning to the club as sporting director.