The Colombian ace shone in Serie A last term with Fiorentina and again impressed with his nation at the World Cup.
Despite strong links with United over the summer, Cuadrado signed a new contract with La Viola, which includes a £26.8m release clause, which Chelsea are believed to be ready to match.
Negotiations are under way, and Jose Mourinho is thought to be keen to get the flying winger to west London before the end of the month as he plots to build on his side’s advantage at the top of the Premier League.
Financial Fair Play worries are set to be eased by the exits of Andre Schurrle and Mohamed Salah, while fringe player Marko Marin has joined Anderlecht on loan.
Cuadrado, 26, has been lauded for his pace and trickery and is considered to be one of Italian football’s finest talents.
Although primarily a right-winger, the South American can also play at right-back or on the left flank.