Hart, 62, became Leeds academy director last September, but left the Elland Road club earlier this month.
"He's someone I would love to bring to the club for lots of reasons," Jones told BBC Three Counties Radio.
"I've always gone to him for advice and I always wanted to work with him again. He's someone I respect highly."
Hart previously worked with Jones at Charlton Athletic.
"Probably one of my best years in football was with him at Charlton," Jones continued.
"He's been a bit of a mentor for me. If there's a possibility that we can do something then that would be a really good addition to our team."
Luton Town manager Nathan Jones hopes to recruit former Nottingham Forest boss Paul Hart to work alongside him at Kenilworth Road.