Questions: How long has the employee been working for the organization? Did the current supervisor hire the employee, or inherit him? Why is the manager concerned about firing a team member who is not working out?
If the employee is brand new and the fit just isn't there, then have the manager sit down with him and with you to have a frank conversation that it is not working out, pay two weeks in lieu if you wish, and let the employee go.
If this is a longer term individual and this dance has been going on for a while (and especially if the current manager was not the hiring manager), then I would probably put the employee on a very short performance improvement plan - written, of course! I would specify what he is doing that he shouldn't be or what he isn't doing that he should be and let him know that immediate and sustained improvement in those areas is expected or he may lose his job. Make it clear that his performance will be monitored for the next week (or two, or whatever timeframe you and the supervisor agree to), and then if he still isn't making it, let him go. I would probably still offer pay in lieu of notice in that case, but it really depends on the dynamics of the situation. In some cases, severance may be the way to go, regardless of the fact that it is excluded from wages in lieu of notice for unemployment purposes.
My bottom line in all of these situations is "can this employee be saved?" You can't expect them to read minds, and if the supervisor has been so gentle with the employee as to not be clear about how tenuous his employment situation is, then I think a little more effort should be applied.
I'll be curious to hear how this works out!