Could there ever be a carrier borne F-22?

The Navy  funded $165 million in R&D in the early 1990s to investigate development of a nasalized F-22, but the project never went beyond the research phase.

The biggest problem is that the F-22’s landing speed is too high for landing on aircraft carriers, and solving this would pretty much require turning it into a swing-wing fighter. Doing that and keeping the F-22’s stealthy characteristics wasn’t considered reasonable or affordable, as you’d wind up designing basically an entirely new aircraft.