Hope, who is a free agent after being released by Gillingham, is one of five players currently bidding to impress new Bees boss Leroy Rosenior.
He is joined by midfielders Paul Smith and Danny Kedwell, goalkeeper Nathan Abbey and winger Dave Lawrence.
Hope left Glanford Park in the summer of 2000, following United's relegation from Division Two, in a £275,000 move to the Gills.