Solskjaer's side travel to Newcastle United on Saturday afternoon in a game that they need to win to stand a chance, and the Norwegian said that it would be an even bigger achievement than Manchester United's late turnaround in the 1999 Champions League final.
"If we stay up it would definitely be a bigger miracle than Barcelona in 1999," Solskjaer told Sky Sports News. "That night it was possible, and in football anything is possible. So we need to give ourselves a chance in front of our fans against Chelsea.
"It takes belief, togetherness, a team that goes the extra mile, and a hero stepping forward and doing something magical.
"It's still possible that we are out of the bottom three if we win this weekend. We have got to give ourselves something to play for in the last game by winning this game."
Cardiff are currently one point behind 19th-placed Fulham.