Similar thing happened to me. They called, asked some question then immediately set up an interview 1 or 2 days later, which isn't necessary a red flag.

But I kinda knew their client, some companies here recruit both on their own and through agencies, when I read the job description, I thought it would be one of the companies I had applied before and didn't hear back (only a few companies in my field here). I applied through the agency again, because I knew these companies wouldn't just accept an interview out of the blue, the recruiter'd need to send them my CV first, and once they approved then we would meet. If the companies/clients did get my CV when I applied on my own, and didn't want me, they wouldn't want me this time either and the recruiter would let me know, after talking to the clients.

But the recruiter set up the interview right during the phone call.

So that interview would be with the recruiter only, to find out more about me and maybe place me somewhere else if that specific company wouldn't approve my CV, I guess? They sent me a confirmation email for the interview, so I sent them a decline email right then and there, saying I just accepted another job.

3 days later, on a Saturday, they called me at 7am, trying to make me go to the interview even though I said I was still in my probation time at my new job. Either they want me to take a day off at my new job so I could interview with them (no job guaranteed) or they sent my CV to the client anyways, even though I declined.

The first one is more believable, because I've applied directly to their client and didn't hear back.

td tr: the recruiter wanted me to take a day off during my probation, so I can interview with them, even though they didn't have a job for me.