If a bank sells a banking location to another financial institution and wants to credit interest to a particular account type before the transfer of the accounts, is it alright for the new bank to send the 1099-INT for interest credited by the selling bank and the new bank at the end of the year? Is there any requirement for the selling bank in this regard? Thank you.

According to the IRS General Instructions, it can be done either way. I think in most cases, whomever is holding the account at the end of the year does the reporting. That doesn't have to happen, though. See page 6 of this document:
http://ftp.fedworld.gov/pub/irs-pdf/i1099gi1.pdf