What do you mean by a man asking you to contact him more if you have nothing to do?

A large part of it is polite. If you don't have feelings for him and you won't have contact with him in your life and work, then leave him alone!

If you don't feel anything, but you have contact in your life and work, say hello when you meet, talk if you have something, and don't talk if you have nothing.

On the contrary, if you have feelings for him, you should take the initiative to talk to him about your situation at ordinary times and ask him out to play during the holiday.