The England Under-21 international will miss the start of the season, and Redknapp has admitted he wants a new full back for cover, which could also lead to Taylor moving up to the left side of midfield.
However, target Graeme Le Saux has chosen deadly rivals Southampton over Pompey and the club is denying putting in a bid for Lens defender Cyril Rool. Redknapp has now made a new left back a priority, along with a midfielder and striking cover.
Chairman Milan Mandaric has vowed to make money available to improve the squad further, but cautioned: "at some point, we have to draw the line, because that is how clubs get into trouble".