The 25-year-old, who joined for £2m from Werder Bremen last January, is wanted by the German club to replace the recently departed Rafael van der Vaart.
And the Danish midfielder could be persuaded to make the switch after admitting his chances of first-team football are limited following the arrivals of Zoltan Gera and Andranik Teymourian.
Andreasen said: "It is a difficult situation in Fulham.
"There are many of us are fighting for the two starting places in the team."
Andreasen made just 13 appearances last year as Fulham escaped relegation from the Premier League on the final day of the season.