PA-28 Flight Instructor reported a NMAC while on base leg with a Lear Jet on a straight in approach.

Narrative

Incident occurred during full stop taxi-backs with a student. Departed runway XXL and was given instructions for right traffic; which has aircraft cross over the final for XYR during base and land back on XXL. This is normal for operations at ZZZ. Prior to my takeoff clearance a Learjet 45 was cleared to land; which was on the visual or RNAV approach for XXL. I was demonstrating a pattern to my new student; and I was the only aircraft in the pattern; so I had assumed I was continuing my approach to XXL as I had not been contacted by ATC since my takeoff clearance to either change runway; or extend my downwind. During by the time I had reached the normal base turn distance I had forgotten that there was one other aircraft landing on XXL as it had been several minutes since the jet had been cleared to land and I had not been given any traffic call by ZZZ tower. At this point the Learjet had been in my blind spot from my right seat position as I was making right turns and I was focused on teaching my student during the time I believe it would have been possible to see it. At this point during my base turn my student had alerted me to the oncoming aircraft to which I was not able to see at that current moment due to it being in my blind spot. I immediately turned right to align myself up with XYR and looked off my left wing to see the Learjet parallel; roughly 20-50 feet under my aircraft and about 300 feet to the side 5~ seconds after I had turned; (I believe this is roughly the centerline-to-centerline distance between XXL and XYR at ZZZ.) I was not given a runway option clearance until I had aligned my aircraft final for XYR and was roughly half a mile from the runway threshold. This added to my confusion as I would have normally expected a runway change due to incoming jet aircraft to have occurred early into my downwind leg as I was the only aircraft operating in the traffic pattern. I believe if my student had not noticed the aircraft I would have continued my base and positioned myself to be on a collision course with the oncoming jet as I had not been given any indication from the controlling tower to change runway or a traffic call until I had already established myself onto the parallel runway.