The Hoffenheim goalkeeper, 36, told Bild he has already been in contact with Klopp regarding a possible call-up for next week's fixtures.
"Yes, I've had contact with him. Everything else he will announce on Thursday. We'll see what happens, that's up to him," Baumann said.
Baumann has long been part of the national team set-up but has made just 13 appearances to date. He took over the club's number one spot last autumn, only to be dropped shortly before the World Cup by former head coach Julian Nagelsmann in favour of Manuel Neuer, 40.
Klopp, who took charge of the national team over the summer following Nagelsmann's departure after Germany's shock exit at the World Cup, has previously suggested he wants to give a number of new and younger players an opportunity in goal.
Speculation has recently circulated around potential call-ups for Loris Karius, 33, of Schalke 04, Jonas Urbig, 23, of Bayern Munich, Finn Dahmen, 28, of FC Augsburg, Noah Atubolu, 24, of Eintracht Frankfurt, and Diant Ramaj, 24, of FC Copenhagen, as Klopp looks to reshape his goalkeeping options.
Baumann, however, has repeatedly reaffirmed his own availability and willingness to be considered, regardless of the direction Klopp ultimately decides to take with his goalkeeping options for the upcoming Nations League fixtures.
Klopp's first match in charge of the national team comes against the Netherlands later this month, with his squad announcement on Thursday set to offer the clearest indication yet of his plans between the posts.