The 51-year-old has been out of work since leaving his role as Bulgaria manager, and described potentially succeeding Craig Levein as an "interesting challenge"
Levein was relieved of his duties after Scotland began their 2014 World Cup qualifying campaign by gaining just two points from four games.
And Matthaus, who has been out of work since seeing his contract with the Bulgarian FA not renewed, has now thrown his ring into the hat for the role.
“My management has been in contact with the Scottish FA,” he told reporters. “My name is known in Scotland.
"We haven’t had any specific talks yet, but Scotland is a football-loving country, and this would be an interesting challenge. I expect to be back working as a manager in January.
“Already, I have some interesting proposals from clubs and countries, but let’s wait and see.”
Matthaus, who is Germany's most-capped player of all-time with 150 appearances, also previously gained two years of international management experience with Hungary.