Reading the rumor sites is a guilty pleasure of mine, and I have not heard much if anything about it.
The current model can be had from an authorized dealer for $1800 or even slightly less, but I bear no hard feelings for having paid $2,500.00 for my copy as it is such a beautiful and smooth lens and I've gotten 5 great years worth of photos from it. I can't see waiting for a new version of a superlative lens that needs no improvement.
"...the mk1 came out in 2001 and then the mk2 in 2010..."
Canon comes out with a new lens when they have a update or design update. Not on a time schedule. There may never be a Mk III. Besides even if they do, how many great shots are you missing by waiting?
There won't be a 70-200mm 2.8 IS III anytime soon for the same reason there still isn't a 70-200mm 4.0 IS II....
There is no need for either one.
The 70-200mm 2.8 IS II and 70-200mm 4.0 IS are both just about perfect.
How do you improve on perfection?
09/26/2023: New firmware updates are available.
08/18/2023: Canon EOS R5 C training series is released.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
03/30/2023: New firmware updates are available.