The Sweden midfielder arrived on-loan from Spartak Moscow carrying a back injury.
Parlour told the London Evening Standard: "This is a crucial time of the season with games coming thick and fast. You need extra bodies now. Arsene Wenger knew the gamble he was making and has made sure that Arsenal only have to pay half his wages until he's fit - once he is fit I think he will be a good singing for the club.
"Kallström has got experience and can also help the younger players in the squad. When the pressure kicks in with eight games to go, every single point is important and experienced players like him can help players like Wilshere."