I live in a 2-story home on a concrete slab. My washer connections are in my garage. We are considering a remodel and want to swap the kitchen and garage. The current kitchen sink is on an exterior wall and the washer is in the garage on an interior wall that is behind a bathroom. The kitchen and garage are perpendicular to each other. The hardest part is how to drain the washer in the kitchen and the kitchen sink in the garage. I do not believe the washer is vented on the roof.
Any suggestions? Thanks for the comments so far!

You have just about narrowed you options to installing the washer and the kitchen on the opposite wall. The less expensive way to go is to use the existing kitchen stack for both your washer and your kitchen sink. Simply stub out your sink at about 18" and your washer at 4" and stub it out opposite the sink. You have just reversed your fixtures and as I understood the question, that's what you wished to do. If you wish to do more it will consist of reruning the drainage and perhaps the vent
I want to take this opportunity to welcome back Labman who has been sorely missed, Welcome back !! Tom

If you can't make Tom's idea work, don't give up. For maybe $100 and a hard days work, you can rent a saw, cut the slab, reroute some of the lines and pour new cement. Just be sure to use traps and vents as needed, and keep any long horizontal runs sloping down at least a little.