Last I checked, Southwest doesn't care a whit about Ryanair. They care about competing in the US and here they have the lead.
But it is interesting to note that Southwest's "low-cost" reputation is, at this point, mostly based on memory and advertising, not reality.
Southwest often isn't the lowest fare on a given itinerary anymore, for example, and airports where Southwest is the dominant carrier are also, mostly, those which have seen the largest fare increases over the past decade.
And that's without getting into the fact that Southwest is now experimenting with ancillary-revenue programs through things like buying into Group A, etc.
The RyanAir equivalent in the US today is Spirit.
I find that very often United fares are lower than Southwest anyway. Perhaps it's because SFO is their hub.
Virgin is another surprise - a couple times I've ended up getting SFO -> BOS or SFO -> JFK flights that are cheaper than anything else on Virgin America, even though it's supposedly a "premium" airline. I think they may be offering specials to build up repeat customers on the route, though.
Since RyanAir has shown some prowess in this regard (admittedly through solicitation of subsidies, but also with an aggressive model), Southwest would certainly have some interest. We're talking almost 50% greater net profit on a third of the revenue. Sure that exact comparison is debatable, but the contrast is nonetheless interesting, even if done with a novel approach.