Should I offer to hire my former boss?

5 years ago, I was hired as a production manager. My boss at the time (Mr K), head of production and his boss (Mr T), head of operations (production + other departments like quality, maintenance etc.). Mr K and I got along great, he's only a few years older than me and we have a similar mindset and work ethic.

2 years ago, I was offered a position as head of production at another company but within the same industrial site. My boss there is Mr J, head of operations (same setup). So I am currently on the same level as my former boss and we are still on very good terms. We meet regularly at site-wide events or at the lunch restaurant.

Now, end of last year Mr T retired and instead of offering Mr K the head of operations position the company brought someone from outside, Mr E. According to all my former colleagues, Mr E is a major a**hole. I know from Mr K personally that he wants out of there quickly. My boss Mr J will retire in summer and I have already been offered & accepted to become head of operations - leaving me with an open head of production position to recruit for.

Should I offer the position to Mr K as he would be the perfect candidate or would that be too weird considering he was my boss just a few years ago and now I would be his boss?

UPDATE: Thanks everyone! Happy to hear that most of you think it's OK to ask him. After all, he can always just say No if he feels uncomfortable with me becoming his boss. I've got a meeting with our head of HR and my current boss coming up where we'll finalize my paperwork for the promotion and also talk about the hiring strategy for my successor. I'll bring it up there that I think Mr K would be a great candidate and if they are not totally against it I'll talk to him. We'll still put the position on our career website/ the usual hiring portals in any case.