Maguire had been watched closely by the Hammers for some time and finalised his move to the East Londoners yesterday,
Joe Cole's return to Upton Park was to be confirmed today after he underwent a medical at the club's training ground yesterday.
The Hammers expect to complete the paperwork in time to to ensure the 31-year-old will be available for tomorrow's FA Cup third-round tie against Manchester United.
Cole's deal must be lodged before midday to confirm his availability against United and set the scene for his return to Upton Park after almost 10 years.
Should the deal go through, it will end a nightmare two-and-a-half-year spell at Liverpool for the former Chelsea player. Cole has started just nine Premier League games since he swapped Chelsea for Liverpool in the summer of 2010, and spent last season on loan at French club Lille.
Reds boss Brendan Rodgers deemed the Londoner surplus to requirements when he took over last summer and Cole is keen to go back to Upton Park, where he spent four years in the youth system before going on to become a first-team star for five seasons.
Reports last night also suggested the Hammers had made a bid for Arsenal striker Marouane Chamakh