The 22-year-old suffered an ankle injury during Liverpool’s memorable 4-3 win over Borussia Dortmund earlier this week.
“I am a fighter and won’t let anything get me down,” he told the SID news agency in his homeland.
“I will give everything to try and be fit in time for the Euros and I am optimistic about achieving my goal.”
Can was called up to the German national team for their last two friendlies against England and Italy.
Jurgen Klopp will now be unable to call upon two key midfielders following the latest injury to captain Jordan Henderson who is out with damaged knee ligaments.
Liverpool will take on Villarreal next in the Europa League semi-finals but if they do progress to the final Can may just recover in time as it will be played on 18 May.