What would you do if a company recently rejected you contacted you for an offer?

So a company I recently interviewed with rejected me because they chose another candidate (No automatic rejection email. Both the recruiter and the manager emailed me saying how difficult it was to decide who to hire and all that in a polite way) but a few weeks later the manager emailed me back saying another candidate rejected the acceptance and asked whether I'm still looking for a job (also politely).

However, I am currently in the middle of the interviewing process with another bigger company and would like to finish the process (currently second technical phone screen).

How should I handle this situation?

Should I tell them I want to work for them but still would like to finish the interview first and then ask for a written offer via email and tell them to wait for a few weeks?

Thank you!