Right full-back Alcock, 26 is currently a free agent after leaving Peterborough United this summer - although it is understood that the Cornish born defender was offered a new deal by the Posh but he declined.
The Blades are currently without a right full-back after Tony McMahon joined Blackpool last January and John 'The Beard' Brayford returned to Cardiff City following the end of his loan spell. Alcock would become the Blades sixth signing of the summer.