The Liverpool Echo says left-back was a problem position last season and it's an area Dalglish is keen to address.
Having already moved smartly in the transfer market to complete the signings of Jordan Henderson, Charlie Adam, Stewart Downing and keeper Alexander Doni, a left-back is likely to be Dalglish's next priority.
Paul Konchesky was sold to Leicester City last week after a miserable spell with the Reds, while Fabio Aurelio has been dogged by a succession of injuries.
Glen Johnson performed solidly on the left when needed last season but the England international is at his best on the opposite flank.
Emiliano Insua has returned after his loan spell at Galatasaray and played in last Saturday's 6-3 friendly win over a Malaysia XI in the Far East.