The Manchester Evening News says Ferguson has been monitoring Cole since contract negotiations stalled at the start of the year.
Cole will be officially available on July 1.
Ferguson believes his versatility could make him a crucial part of his plans to wrest the Premier League title back from Chelsea.
The biggest threat to United's hopes of landing Cole is his desire to stay in London.
But he is also desperate to add to the three titles he has won at Chelsea as well as lift the Champions League for the first time, which could give United the edge.