Hazard's future has been up in the air since last summer, when he was linked with a big money move to Real Madrid.
"He's been our talisman, he's been excellent over the time he's been at the football club," Walker told Love Sport Radio.
“He's a pleasure to watch. He's an all-round nice guy. It will be a severe loss to Chelsea to lose him if he did go.
“In some respects, being an ex-player, I understand why he would want to go but he seems very happy at Chelsea.
“I think happiness goes a long way when you reflect back on your career.
“Hopefully we'll keep him for a few more years yet."