The former Chelsea left-back's departure from the Italian club was confirmed on Tuesday, bringing to an end an 18-month spell during which he played only 11 games in Serie A.
Sources have told Goal that Cole will not have designated player status with the Galaxy and nor will part of his contract be paid off with targeted allocation money, a new mechanism that allows MLS clubs to convert designated players into non-designated players by reducing the amount of their salary that counts against the salary cap.
The 35-year-old will join his former England team-mate Steven Gerrard - who, in comparison, earns more than $6 million a year - in California as part of a high-profile core that also includes ex-Tottenham striker Robbie Keane and Mexico international Giovani dos Santos.
Cole played 107 times for England before retiring from international duty in 2014 after missing out on a place in the squad for the World Cup in Brazil.
The Galaxy have also been linked with AC Milan midfielder Nigel De Jong and Standard Liege defender Jelle van Damme following the departures of Juninho and Omar Gonzalez.
Goal understands any move for De Jong would initially be on loan as the Netherlands international has multiple years remaining on his contract.