The Brazilian midfielder has begun training with Eintracht in recent days - on recommendation of Klopp.
BILD says Klopp tipped off Bobic about the Reds midfielder, who cannot be registered in England due to work permit difficulties.
A loan deal is being proposed which would include a permanent option.
Eintracht coach Adi Hutter said: "We know that he can play football. We now have to get a good picture of him in practice and will let him play in the two friendly matches - maybe even longer than others.
"It is also possible that he will stay with us in Frankfurt for a few days afterwards."