Reds boss Kenny Dalglish hopes to sign the player, who has made three appearances for England, before the end of the transfer window on Wednesday, August 31.
The 25-year-old has been linked with a number of clubs, including Arsenal and Chelsea, during the summer but Liverpool have made their move.
Bolton are understood to be holding out for a fee of £17m for Cahill, although Liverpool will offer David Ngog as a makeweight to the deal.
The Reds confirmed the signing of Jose Enrique from Newcastle on Friday.
Liverpool open their Premier League campaign with a home match against Sunderland on Saturday.