Argentina international Emiliano Insua is on the verge of leaving Liverpool and signing for Fiorentina as Reds boss Roy Hodgson steps up his search for a new left-back.
Fabio Aurelio was released earlier in the summer, leaving Hodgson without a senior left-back.
The former Fulham boss said: "We're short and that is going to be one of the priorities. We need to find a replacement for Emiliano and Fabio. That's one job we'll have to do.
"As far as we understand, the deal (for Insua) has been completed between the clubs and his agent is sorting out personal terms. Maybe it was the right time for him to move on."
Meanwhile, Hodgson has played down speculation linking Javier Mascherano with a move away from Anfield.
The Argentina international is currently on holiday after his exertions in the World Cup but has spoken at length of his desire to leave Merseyside, with Inter Milan his preferred destination.
However, Hodgson added: "He doesn't need to make contact with me. I've made contact with him telling him I'm looking forward to seeing him in training when he returns from his holiday but I did make the point in the voicemail that I didn't expect him to contact me.
"I just wanted him to know that I'd been in touch and that I was thinking of him. I didn't ask him to call me back. I don't have a lot to say to him, to be honest, other than 'Welcome back'."