The defender reaches the age of 33 in November and at the end of this season his current deal runs out.
There has been doubt cast over his future at Old Trafford because of injuries he keeps picking up, and also the fact that Chris Smalling and Phil Jones look to be the future at United.
This has fueled speculation.
Speaking to Goal.com a source said: "The Fire are interested in Ferdinand.
"We have watched and admired the play of Rio Ferdinand for a number of years, and we would be thrilled to have a player of his quality join the Chicago Fire Soccer Club."