The free-scoring striker will be out of contract in the summer, but he is keen to stay with an Eagles side that has hit form at just the right time.
"In an ideal world I would like to stay," Morrison told the South London Press.
"I'm a London boy and I know what this club is about. We've got a great chance of playing in the Premier League which is where I want to be again.
"The first time up there wasn't so good for me at Birmingham, I was in and out of the team. But with this group of players and management team we've got a good chance. If it came to signing I probably would.
"At the moment I'm happy and just want to play football. The contract's not something that's on my mind.
"It's up to the club to come and talk to me - I'm not going to go to them and talk about it. I'll just keep doing what I'm doing and hopefully I'll be rewarded for it."