The Welsh outfit are in danger of being relegated to the Championship due to currently being placed second from bottom in the Premier League table.
Following last weekend's 3-0 defeat to Crystal Palace, the Bluebirds are six points adrift of safety with five games left to play.
"He's there now, give the lad time and see what he can do," BBC Sport quotes Rush as saying. "If Cardiff do get relegated - hopefully they don't - you say [to Solskjaer] 'your job now is to get us back in that Premiership' and give the man a chance to do that.
"When you get rid of a manager it's a gamble - sometimes it works and sometimes it doesn't."
Solskjaer was appointed in January following the dismissal of Malky Mackay.