What FabFiona said - don't put them on, have them "by request" then when you're asked for them, ask for 24 hours to let them know. You're allowed to be up front with the new organisation. Or let the referees know when you've got an interview. Hopefully they're circumspect.

I've only once told my work I'm looking, and that was because I needed an ongoing position, not a contract any more.

Good luck!