Unfortunately, it does not appear you could help him obtain lawful permanent residence. You could file an immigrant visa petition on his behalf but it would be useless to him as he could not use it to seek a green card. The reason is that to apply for a green card based upon an approved employment visa petition while in the United States you have to establish you were admitted and that you maintained lawful status during your entire stay.
Your employee may have other options depending upon more information about his circumstances. I would recommend you help him by getting him in contact with an experienced immigration attorney. However, please keep in mind that some times leaving well enough alone is the best course of action.
Answered on Jun 15th, 2016 at 3:31 AM