A Spanish newspaper reported that Casillas, currently at Portuguese giants Porto, has signed a pre-contract agreement with the Merseysiders despite offers from Turkey, Qatar and China.
Liverpool baas Jurgen Klopp has been looking for a new goalkeeper after inconsistent performances by current options Simon Mignolet and Tony Karius.
Casillas is the latest goalkeeper to be linked with a move to Merseyside after Liverpool have also been linked with English stopper Joe Hart.
If Casillas joins Liverpool then the 36-year-old stopper will be able to add to his record 164 appearances in the Champions League, which was earned through stints with Porto and Real Madrid.
He spent 16 years with the Spanish giants.