Favre was fired in the wake of Hertha's disastrous 5-1 defeat at Hoffenheim on Sunday which left his side rooted to the bottom of the table after last week's 4-0 hammering at home to Freiburg.
Daily Bild reported on Tuesday that officials were now considering hiring the 48-year-old Matthäus, who is currently coaching Israeli club Maccabi Netanya.
"There has been no contact with Hertha, but it would be great to work in the Bundesliga," he said.
Matthäus won the World Cup with Germany in 1990 and is the most capped German player of all time having made 150 appearances for his country.
But the former midfielder has a reputation for being difficult to work with having coached Rapid Vienna (2001-2002), Serbian champions Partizan Belgrade (2002-2003) and the Hungarian national side (2004-05).
He then spent just 33 days at Brazilian club Atletico Paranaense before working with Giovanni Trapattoni at Austrian club Red Bull Salzburg, but he was fired after a year despite the team winning the national championship.
Hertha, who finished fourth last season, have garnered just three points from seven games this term since Favre, who lifted the Swiss title with FC Zurich in 2006 and 2007, allowed three key players to move on in the summer.
They included skipper and Croatian star Josip Simunic, who joined Hoffenheim, while another key loss was Ukrainian forward Andrei Voronin, who returned to Liverpool following a loan spell.
Hertha's youth coach Karsten Heine will now have to pick the players up for a midweek Europa League match against Sporting Lisbon before the club tackles Bundesliga leaders Hamburg next Sunday.