The former Reading youngster was one of Town manager Paul Jewell's top transfer targets during the summer as he looks to reshape his Portman Road squad.
However, Henry impressed for Millwall last season and manager Kenny Jackett is determined to keep the 21-year-old at the Den.
Jewell has admitted that his club are unlikely to make a third offer for the player and he is now assessing other options.
"We have had a bid for James Henry turned down by Millwall," said Jewell. "That was the second bid we've put in.
"It's been rejected by Millwall and they've told us he's not for sale, so that's probably a dead one. We're looking elsewhere."
Jewell took over the managerial reins at Ipswich in January of this year.