The 32-year-old, who scored twice in eight appearances for his country between 2005 and 2006, is currently without a club after leaving Cardiff City last December.
According to the Southend Echo, Richardson has linked up with the Shrimpers on a trial basis, and will continue to train with the Essex outfit until a decision on his future is made.
Richardson scored 11 times in 81 appearances for Manchester United between 2002 and 2007, before leaving to join Sunderland, where he spent five years.
The versatile midfielder has also previously had spells at Fulham and Aston Villa.
Another former England international - Carlton Cole - was recently training with Southend, but the 33-year-old "disappeared off the face of the earth" after a short trial with the club, according to head coach Phil Brown.