Palace are searching for a new boss after the departure of Ian Holloway and are currently bottom of the Premier League after collecting just three points from their opening nine games.
Former Birmingham and Aston Villa manager McLeish believes that Palace can avoid relegation, but has denied that discussions have taken place with chairman Steve Parish.
"There hasn't been any contact yet but I am available as a free agent," McLeish told Sky Sports News.
"Crystal Palace are in a position that's precarious for them but there's still a lot of points to play for.
"I've had those kind of challenges before and I've had some success and some failures, but if you've got a fighting spirit and good players playing to their strengths, then why can't Palace stay up?"
McLeish's last job was at Nottingham Forest where he left by mutual consent in February and has not ruled out the possibility of coaching outside of the UK.
He said: "I've watched a lot of games, I've visited friends who coach abroad and have kept my finger on the pulse.
"I'm fresh again. I'd like to have a crack at somewhere, maybe even abroad."