I will give you an advice (12 years industry experience) which hopefully you should remember forever:

No one is looking out for you except YOU. PERIOD.

Don't forget this rule above. If your boss decides that they don't want/need to hire you at the end anyway, you are screwed.

Tell your boss "I look forward to working with you if it happens" and then keep applying wherever you need to apply. Your boss may mean well but at the end of the day, he has to report to someone and he has to look out for himself/herself.

Never ever put your career in anyone else's hands except yours.