Dembele looks set to stay at Barcelona despite a tumultuous two-year spell at the Nou Camp.
But Murphy thinks the Reds should target Dembele as he would be an improvement on Brazil international Firmino.
Murphy told bwin: "Dembele would be a fantastic signing for Liverpool. He's not had the best time at Barcelona, but clearly has an abundance of talent and the ability to win games by himself. If he can recapture his belief in his ability, then Liverpool would have a formidable front three with him, Mane and Salah.
"When playing to his potential, I think he would edge Firmino out the first team. Firmino is the type of player that would raise his own game and everyone's around him if Dembele came in to the team. He'll fight for his place week in week out and if you're not giving your all on the pitch, then Firmino will be right there to take it."