The Canaries are short at the back with Jason Shackell out and veteran Dion Dublin unlikely to be thrilled at the prospect of having to play every game in a hectic September and October schedule.
Grant confirmed that Hall was one of the players he has looked at, but that loan moves present problems in themselves.
"We are always interested in good players and Fitz Hall is a good player. He is one we've looked at," said the Norwich boss. "But a lot of clubs are interested in players and 90% of the time you find yourself having to pay a transfer fee as a loan fee. A loan player from the Premier League would cost Premier League wages, but the search continues no matter what."
One solution could be to set up a similar deal to that which saw Dickson Etuhu move on loan before a permanent deal was officially struck, although how strictly within the transfer window rules that sort of deal is remains cloudy.