If I say: He is really into this job, does that mean he’s interested in this job, or he’s working hard on this job?
It can mean that he really enjoys his job and is very interested in it. “He’s really into his job. It’s his main interest, and it’s both his career and his hobby.”
It can also mean that he is in the middle of doing his work and is concentrating very hard. “Don’t bother him right now. He’s into his job.”
I would say: ‘he is after that/this job’.
No, as Conchita says, he’d be desperately after the job.
I’ve got it finally!