My advice - it sounds like you're worried about jeopardising your current job, so I would recommend you just say "references available upon request." I do this and it's never inhibited my opportunity to secure a new job.

The prospective company will usually only want to speak to your references near the end of the process and if they're interested in hiring you.

If they ask for the references early, you can provide your non-current references and explain the situation about your current ones. Most recruiters with common sense will completely understand your reasons.

Of course, there are exceptions. For example if you've got a good relationship with your current company and you've had open conversations about your need for growth, you can be proactive, just like /u/ChelsG was, which could in a promotion/pay rise at your current job.

But, if the opportunity isn't something you can get at your current employer, you shouldn't risk them knowing until you're more or less guaranteed to get the new position. Good luck!