O'Shea, 28 has scored 8 goals in 33 games for Chesterfield despite battling against relegation. He joined the Spirites initially on loan from MK Dons in 2012.
Like Hanson (Bradford City), he is out of contract at the end of the season and Blades boss Chris Wilder is looking to bolster is squad ahead of a promotion push.
It is hoped that both Hanson and O'Shea will be available for selection for tomorrow's home fixture with Fleetwood Town.