Cole is a free agent after he failed to agree a new contract at Chelsea.
The midfielder, currently in South Africa with England, has insisted he is leaving talks of his future down to his representatives.
Arsenal and Manchester City emerged as favourites to sign Cole earlier this summer, but lately it was United who were widely reported to have won the race to land him on a free transfer.
Tottenham boss Harry Redknapp said earlier this week that he felt a deal to take Cole to United was all but done.
But now both Sky Sports and the BBC claim that Cole will not be heading to Old Trafford this summer.