26-year-old Allsopp was first linked with the club a month ago, but the reports were denied. Since then, he was given a rare start for City, against Wrexham, and he scored both goals in a 2-0 win to take his goal tally to 22 since joining City from Notts County last year in a deal worth around £90,000.
He kept his place in the team for the next game, at MK Dons, but that was to be the last time he appeared in City colours. He made 67 appearances in all.
Peter Taylor isn't expected to bring in another forward following Allsopp's departure, after recently paying around £125,000 for Craig Fagan.