The Premier League trio were all interested in the Chilean attacker during his spell in Serie A with Udinese, but were unable to compete with Barca, who tied up a £22m deal for his signature in 2011.
However, despite impressing in his opening campaign with the Spanish giants, Sanchez has struggled this term, netting only four goals, with Cesc Fabregas, Pedro and Lionel Messi enjoying the lion’s share of game time in attacking positions.
This has led to speculation that he will be allowed to leave the Catalans this summer, news which has sparked interest from a number of top European sides.
Liverpool were linked with a loan move for the South American ace during January, but Barca were keen to keep hold of him.
The Reds will unlikely be able to compete with City, United and Chelsea for a permanent deal, however they will face strong opposition in the shape of Juve.
The Italian champions are believed to be willing to spend big to snap up Sanchez after agreeing a deal to take Fernando Llorente to Turin at the end of the season.
But, the English clubs will be able to match their offer, which could spark an intense battle for his signature.