The American team are desperate for a high-profile English player to enable them to compete with Beckham’s LA Galaxy, and have identified Ferdinand as their main target.
Ferdinand will be 33 next month and is out of contract at Manchester United at the end of next season.
Chicago want the England defender to join them next summer and believe they can persuade him to turn his back on the Barclays Premier League to finish his career in the States.
The former Leeds and West Ham favourite has struggled with injury for the last three years and has been left out of the England squad that flies to Montenegro for their final Euro 2012 qualifier.
Lower US tax rates mean that Chicago would be able to ensure that Ferdinand’s take-home pay would be similar to the money he earns from his £120,000-a-week Old Trafford deal.