Is It Ok To Just Go To The CEO

I’m a senior who didn’t get a return offer at my SA and picked up a winter internship at a pretty lean boutique. They usually offer a decent SA return offer rate but lowered their this year with the economy and other shit. I spoke to the CEO of the firm a decent amount of times just running into him at the office and we had a few good conversations. He always complimented that I was always first in last out, and at the end of my internship told me to keep in touch. I just found out that due to headcount, they don’t think they can offer me a return however my feedback was told to be worthy of a return offer. Is it possible to indirectly ask him to push on my behalf. For reference he’s not super involved in the day to day anymore but always around and people listen when he speaks.