Since you need a quick answer, just a free comment with an opinion.
If the position is also open to non-employees of the company, I would
say definitely "no". There is no reason why the company should pay an
employee when outside applicants are not being compensated.
Even if the hourly employee is competing with exempt employees, who
will get paid for the time of the interview, I still think it would be
inappropriate to charge for the time. Hourly employees are paid for
productive work time, not for time spent on personal activities, and
applying for a job within or outside the company is a personal matter.
Asking for pay looks like the person is putting his own interests
above those of the company, which always makes a bad impression.
Presumably, the position is better than the present one - either in
income, responsibility and/or job satisfaction - so that if the
person is accepted, there will be an advantage to him/her that makes
it worth his/her investing that much of his/her own time to be
interviewed - even if the person has been invited to apply for the
position and to be interviewed.
If the employee has to punch the time clock, and has not logged out
for the time of the interview, it would be appropriate at the end of
the interview to ask if he/she should have, to offer to work off the
time by logging off before making up the time spent on the interview.
This would show a willingness to forego pay for the time and allow the
company representative to make the decision.
If the person fills in his/her own timesheets, I think it better not
to raise the question.