Should I ask for job offer after rejecting?

I worked at a co-op throughout the year and left to go to another company for the summer, but I was invited back to work at my co-op after the summer ended. When I left my summer internship to go back to my co-op, I was given a verbal FT offer. The company I interned for throughout the summer took about 2 months after the internship ended to give me an FT offer, at which point I thought I did not receive any offer. Now fast forward a couple of months, my offer was rescinded due to budget cuts, and now I don't have an offer, and it's been tough trying to recruit for another FT role. Should I contact my supervisor at my internship and explain what happened and ask if they would consider taking me back? I connected really well with her throughout the summer, and I also see that the company has a few roles open on their website. What should I do?