The England captain has managed just 145 runs at an average of 24.16 in the Ashes series so far, even though his side have already retained the urn.
Hoggard, a member of the England side which beat Australia in the memorable 2005 series, recalls times when Cook has struggled previously and is confident the Essex man will soon return to his best.
He told talkSPORT: “Cook went through a patch where he didn’t know where his off-stump was and he kept on nicking off.
“Everybody was questioning his technique and asking if he should be at the top of the order but Alastair Cook’s strength is his mental strength and he’s been working really hard with Graham Gooch who he knows from Essex and he's such a solid character he will find a way of getting through this.
Whether he’s having a fantastic innings where everything's easy on the eye or struggling for runs he has that mental toughness and a will to win.”
Rain at Old Trafford on Monday led to the third Test being drawn although Australia will have been encouraged by an improved showing. And Hoggard is expecting more of the same from the tourists’ pace attack when the fourth Test starts at Chester-le-Street on Friday.
He added: “We always knew Australia were capable of taking 20 wickets and their bowling line-up has held its own all the way through the series which shows how good their seamers are.”
Australian Daily Telegraph: The tourists can look forward to the remaining two Tests and the return series in Australia with renewed confidence.
The Australian: There were glimpses of the Australia of old on display here over the past five days, combative, competitive and confident, not the fumbling, bumbling side that reeled away from the massive Lord's defeat confronting the stark possibility that it was just one more loss away from becoming, officially, the worst cricket side Australia has ever produced.