Can MQTT work over bluetooth?

Sorry if a dumb question.

It is just something which may be handy if it can work for very basic messages.

Don't think so. MQTT requires an ip connection and BT does not provide that by itself. Unless there are some kind of gw softwares around that can bridge ip over BT

What I understand...

EDIT: Actually, this may be a possibility but is a bit advanced, never tried it myself so no warranty issued..
http://redtreerobotics.com/ip-over-bluetooth-with-linux/