According to French newspaper Le 10 Sport, Chelsea, Barcelona and Manchester United are all still keen on the winger. United and Barcelona's interest has been well documented over the last month but Chelsea are a late arrival.
Chelsea interest - why?
It's unclear why Jose Mourinho would want to add another attacking midfielder to his squad - he already has the likes of Eden Hazard, Willian, Andre Schurrle, Mohamed Salah and Oscar to choose from.
But a clue could be found in recent transfer reports that claim Schurrle himself is emerging as a transfer target for a couple of Europe's biggest teams.
Teams in for Andre Shurrle
Atletico Madrid are thought to be eyeing the Germany international, as the Spanish giants are flush with cash following the double sale of Filipe Luis and Diego Costa to Stamford Bridge.
But Paris Saint Germain too are keeping tabs on Schurrle, who was rarely first-choice in his first season at Chelsea. He enjoyed an excellent World Cup too, contributing three goals largely from the bench as Germany won the tournament for the fourth time in their country's history.
Van Gaal intentions
Chelsea will have to be quick though, as reports this weekend claim Cuadrado is keen on a move to Manchester United, who are ready to offer as much as €40m to land him.
United boss Louis Van Gaal hinted at another big-money acquisition earlier this week, saying that the club does not have a winger of the calibre of 'Cristiano Ronaldo or Angel Di Maria' at the moment.
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