If you are currently working, let the interviewer know and inform him that you will be resigning from there which may need you to serve the notice period.

If you promise to inform them the next day, do so. Do not delay.

Do not commit to join the next working day just to leave an impression when you have some chores left to be attended which will delay the process.

Be honest and straight as most of the firms are familiar with the procedure of resignation and will grant the time to join them when you have been relieved from your duty from your last working place.