Sky Bet suspend betting on Radamel Falcao's next club after seeing him backed at as short as 1/3 to join Real Madrid.
Morgan Schneiderlin has appealed to Southampton fans after a thwarted attempt to leave St Mary's.
The 40-year-old has signed a contract until 2015 and takes over from Mike Buskens, who was sacked last month.
Kramer has previously coached Furth's Under-19 and Under-23 sides and most recently was in charge of Hoffenheim's Under-23s.
Furth's 3-0 defeat at home to fellow strugglers Hoffenheim on Saturday left them five points adrift at the foot of the table and after the game president Helmut Hack admitted the result left them to "prepare an honourable relegation".
He told the club's official website on Monday: "Even though it is very hard for us after the defeat at the weekend, we now have to look forward.
"With Frank we are getting a coach by whom we were completely convinced. He will drive our new start so that we can look forward with confidence."
Kramer said: "At the moment it is certainly not an easy situation, but we will work day and night to make the best of it."
Ludwig Preis, who has been serving as interim coach, will stay on as assistant until the end of the season.