After missing out on Thomas Vermaelen – who picked Barcelona over the Red Devils – Louis van Gaal was thought to be plotting a £36m move for the Fiorentina man.
Cuadrado shone for La Viola last term and his nation at the World Cup over the summer, and is thought to be seen as the ideal right wing-back in LVG’s new system at Old Trafford.
But now Chelsea are also keen on the South American speedster, and are ready to make a rival bid.
Jose Mourinho is understood to be attracted to the versatile ace – he can play anywhere on the right flank – and has the cash to spend on another big name player despite moves for Cesc Fabregas and Diego Costa.
The Blues may even look to use Marko Marin in a deal, with Fiorentina rumoured to be interested in the German winger.
Cuadrado is said to be keen on a move to Barca, but the lure of Champions League football – which United do not boast – could tempt him to London.