The 23-year-old is being tipped to leave the Portuguese club at the end of the season, but his side are expecting a huge offer before they let him depart.
Danilo currently has a £38.6million release clause tied to his contract, but Brendan Rodgers is looking to seal his switch with an offer around the region of £28million.
The Porto man has made 20 league appearances for his side in the current campaign, scoring three goals and providing one assist.
Should the Brazilian defender complete a move to Anfield, he will join fellow countrymen Lucas Leiva and Philippe Coutinho in the side.
He is likely to be the straight-out replacement for current right-back Glen Johnson, who is set to leave once his contract expires at the end of the season and is being tipped to join Serie A outfits Roma.