Couldn't you simply dig out and re-level the area that has sunk? A drain to move water away from the house is always a good idea.

"Concrete leveling" would be for SLABS, not BLOCKS. That blocks have sunk is not an indicator of bad grade, but merely of base settlement that needs to be fixed. As suggested, remove the blocks, fix the base, and reset them. It would not be "thousands" unless your patio is palatial. If you have a grading condition that needs to be fixed outside of the patio settlement, it would be something you address as well, independently of the patio problem. If you could do the work yourself, since it is mostly labor, it would be very low cost.

If the answers you get don't seem correct to you, provide some pictures of the conditions, including surroundings.

I appreciate the responses. The 2x2 blocks. I should have clarified. They aren’t like pavers. It is concrete and the 2x2 is the seams or joints. That might make more sense.

Do you mean that they were poured in place? It's always best to show a picture or a few ... in order to automatically answer questions.

They are manufactured blocks/tiles, not poured in place. You might call them paving blocks or patio tiles. They look quite worn & weathered, meaning that it might not make sense to spend money on resetting them, only to have an old, near-the-end-of-its-life patio when you're finished. It would make more sense to reset them as a DIY project, since it wouldn't cost much. Or, to suffer along with what you have while saving money for a new patio.

The picture does not show much of the surroundings, but the yard looks quite flat, which would make it difficult to capture water at the patio edge and then run it underground by gravity to a different location. A stop-gap measure could be to install an underground cavity -- a literal French drain -- but that's an iffy proposition (and a fair amount of work.) You don't have any way of measuring the actual volume of storm water that would come to the outer edge of the patio. If the underground cavity was a little shy of handling the capacity, the patio would still flood. It would drain away and dry up quicker, but that might not be enough to justify the effort.

What it would cost to have it reset by professionals would vary, depending on your location and its market for this type work.

I assume its an original patio, house was built in ‘61 but I don’t know that 100%. I had a concrete lifting company come out. The quote was under $1k but he said didn’t seem confident that as he started to lift, that some of them wouldn’t break at the joints. He cuts small round holes and pumps in a mixture to fill what ever gaps there are underneath.

YARDVAARK I appreciate your comments and suggestions. I don’t know what I don’t know. The picture was from 2 years ago I happen to have. I looked this morning and the mulch to the left of the patio furniture, I pushed it back hoping to give the water that accumulates on that end somewhere to go but now it just puddles off the patio and still onto the patio. Another person has recommend putting digging and putting a small drain and pipe in the ground, running it to the right - can’t see it in the picture but water runs better off the top right corner of the patio. So pipe to there and then let it flow naturally with the grade. It slopes so that water goes where it is meant to. We have had A TON of rain this winter In Charlotte

If it's blocks, which are not joined together at their edges other than by abutting, how could the mud jacking process work?

@Yard it may be a slab with the control joints done to look like tiles? We've done that for a few projects, but I can't really tell from this pic. Although I would assume that if multiple landscapers didn't just suggest relaying the blocks, and the mudjacker said they can fix it, it's probably a slab. Maybe? IDK.

IDK, too. If it's a slab, then mud-jack it. OP, watch a video on Youtube about mudjacking.

From what a landscaper said and the concrete lifter guy said, those are control joints. landscaper gave two options—drain and line to move the puddling water away or laying pavers overtop and they’d do that in such a way to level it out so water would drain away. I failed to ask for a price on the paver project but the drain and digging option was also about $800.

So it's possible it's a slab, whereas the choice is jacking or demolition. It will cost more than 800 to lay a new paver patio on top, but it's going to be a better option because your concrete is so worn. Get that price and you will have something to weigh.