Sure, they make floor leveling products that are easy to use.
You better be absolutely sure the substrate is secure though because
those 12" tiles are going to break much quicker than the little 1"
jobs. Any bounce at all on that field and they crack. It's a small
area though and you could do this fast and take the chance.

PS. It probably sagged because water got through and rotted the
subfloor. The rot is still there.