According to Calcio Italia magazine, the Bundesliga leaders are eager to land the Argentine veteran in order to ensure their UEFA Champions League qualification chances.
Apart from Hertha's interest, a good number of Serie A clubs want to run the rule over Crespo at the end of the season.
Genoa, Palermo and Sampdoria are reportedly lining up bids for the 33-year-old, who has become a mere surplus at Inter.
Crespo was once talked into leaving the Nerazzurri by Argentina boss Diego Maradona, who believes the former Chelsea man can regain his peak form elsewhere.
The experienced hitman, who won 65 Argentina caps, hasn't featured for the Tango Dancers since 2007.
However, he's expected to receive a call-up once he moves away from Jose Mourinho's side and comes back into the public eye.