The Welsh outfit seem destined for an immediate return to the Championship after a 4-0 defeat at Sunderland last time out left them bottom of the table, two points adrift of safety with as many games to play.
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However, Solskjaer has backed his side to return from St James' Park with all three points and ensure their fight to beat the drop is extended to their last game of the season against Chelsea.
"It's still possible," he told reporters. "It's still possible we are out of bottom three if we win this weekend.
"We have to give ourselves something to play for in final game and that's not inconceivable. I am confident we can put a performance in up there and hope it's enough because it's not just in our hands anymore.
"The squad here are good lads. They don't feel sorry for themselves. They know it will be hard. It's a difficult position we have put ourselves in but it's possible if we win at Newcastle."
Solskjaer went on to say he believes three points at Newcastle would generate a buzz when Chelsea visit the Cardiff City Stadium next week.
He added: "Just imagine how this place will be next weekend if we have something to play for. That has to be one of key things for us having to beat Newcastle."
But regardless of whether Cardiff avoid the drop or not, Solskjaer insists the future is bright.
"I have no doubt whatsoever about future success for this club," he continued. "The finances and fans we have. Hopefully we get it right and get the help we need to stay in the Premier League next year.
"But this is a club with proper, proper potential. At the moment I'm concentrating on the game tomorrow. But I do think about different things - scenario A and scenario B all the time."