With Andy Carroll being loaned out to West Ham United, Luis Suarez and Fabio Borini are left as the Reds' only recognised strikers and Brendan Rodgers has admitted that he could bring in another forward.
Del Piero is a free agent after being released by Juve at the end of last season and was about to join Sydney FC until the Anfield outfit showed late interest in the player.
A source close to the player told talkSPORT: "Del Piero originally ruled out a move to the Premier League as only Southampton were interested and he didn't want to jump from Juventus to the Saints.
"Then Sydney FC came in and started discussing a deal with him as Del Piero wanted a new challenge outside of top-level football. At the last minute Liverpool came in and said 'don't sign a deal yet as we are interested'.
"The situation currently is that he will not sign for Sydney FC whilst he is waiting on an offer from Liverpool."
Southampton were also interested in signing the former Italy international.