27-year-old Jarrett joined Preston on a free transfer in the summer after playing 11 times on loan last season, but after appearing in the first 6 games of this season hasn't played for North End since.
He's previously had spells with Blackpool, Wrexham, Bury, Wigan - helping them to two promotions, Stoke, Norwich and Plymouth.
Meanwhile, Parkinson does have Danny Coles fit again following a knee injury. He's expected to come in for Mills on Saturday at Southampton.