Personally I'd build it on top of the concrete assuming its in good shape. DO NOT allow the wood to come in direct contact with the cement though. Use a galvanized post anchor. You may have to drill a hole in the driveway and use hydraulic cement to secure it but it should be fine. A TON less work too.

My 2 cents from a regular guy, not a construction expert so its worth exactly that ;-)

With the disclaimer that I'm not a structural guru, your risk of building on a slab without footings below are frost heave, not just settling. Your call on the risk involved and the trade-off.

You mentioned using 4x4 posts, however, and that's not current code. You should use 6x6s, and you don't need 8. Here's a photo of one I helped a friend build that's 10x10. It's free standing, which uses more posts than one done with a ledger board, and we only used 4. You can see how we did the structure with 4 posts, 2 beams, and the joists resting on the beams. 2' cantilever all around.

Ok, thanks guys. All of that makes sense. Thanks for the tip about the galvanized post anchor, cruzmisl. And thank you, weedyacres, for the structuring tips. Good call on the 6x6's. Going against code is the last thing we need... Nice deck, by the way.

"the deck itself will not weigh as much as a car"

Actually it will weigh as much as a tow truck:

11' x 13' = 143 square feet.

The absolute minimum allowable designed load for a residential deck is 50 lbs/sq ft. Many building code jurisdictions will require higher design loads. Standard for light commercial is 100.

143 x 50 = 7150 lbs. You can not assume this weight is evenly distributed over all the footings. It could be concentrated more to one area, under dynamic loads.

I would saw cut the concrete and install correct footings under each post.

If the current slab is at least 3000 PSI concrete you will never generate that force on that deck even with dynamic forces. If your posts are 6X6 then the weight that slab should be able to bear on one post is about 81,000 pounds dead weight. Of course you will only have about 15,000 pounds maximum distributed over 8 posts.
I wouldn't tie the deck to the house though if you are in a freeze thaw climate. The slab will raise and lower during freeze thaws. This might damage the siding or facade.
If the concrete has large voids underneath it then the load it can carry will greatly decrease, and may not be able to hold the deck without cracking. If there is wiremesh in the slab or rebar the flexural strength will be enough to span a small void. Either way the crack wont open up if mesh is properly installed.

I had a new deck built last year but they did not replace the old round concrete footers. Id I’d like to get thise two footers reinf if thats possible

What footers? How was the deck constructed? Where are the footers in relation to the edges of the deck framing?

co these pics help? you can see the concrete cone under the deck, the concrete is old.