What are the reporting requirements for a minister who is not a U.S. citizen, but performs services in the US? Does sending his earnings to his foreign location make any difference?
Depending on several factors, it is likely that this minister is classified either as a resident or nonresident alien. His income is reportable on Form W-2 if he was an employee while in the U.S. or on Form 1099-MISC if he was an independent contractor. Sending the money overseas does not avoid the reporting requirements.
IRS Publication 519--U.S. Tax Guide for Aliens--may be helpful both to the ministry and to the minister. The ministry may also wish to explore Form 1042 and instructions--Annual Withholding Tax Return for U.S. Source Income of Foreign Persons. Also, Tax Topic 851 may be helpful (link provided here).
Probably the easiest way for a local church without foreign tax knowledge to deal with this issue is to advance the funds to the minister's (or to his U.S. sponsor's) U.S. missions agency and let it use its expertise to apply the law.