If you look at their web page it says:
Southwest Airlines Pilot Application Requirements:- Certificates / Ratings: U.S. FAA Airline Transport Pilot Certificate. Unrestricted1 U.S. Type Rating on a B-737 not required for interview but required for employment.
1 The only restriction or limitation Southwest Airlines will accept is "B-737 CIRC. APCH. - VMC ONLY"
2 A candidate may apply without a B-737 Type Rating. If a candidate interviews and successfully completes the entire selection process, he/she has six months from that date to obtain a B-737 Type Rating to be eligible for hire.