The Nottingham Evening Post report that Ward is set to leave the City Ground after finding himself behind new signing Paul Gerrard.
United are still looking for a keeper after Paul Robinson left for Spurs.
Kevin Blackwell has his eye on the Worksop born Welsh international, having already failed in a bid to sign Gerrard.
It is thought talks took place between the two clubs before Forest left for their pre-season tour to the United States.
The 30-year-old, who was David Platt's last signing as Forest manager in 2001, had a back operation over the summer.
The former Notts County and Mansfield keeper missed the end of the season after being injured against Gillingham in February.
