Why don't you sound her out about the job?
Does 'sound her out about the job' mean 'talk to her to see if she want the job' ?
To 'sound someone out' means to get an idea about what they think about something. It usually doesn't mean to come straight out and say "Do you want the job?" It means say something like "How would feel if a new job came up?" You don't put the whole offer on the table. You try to find out surreptitiously what she thinks; whether she would accept it if she were asked.