After trials at Cobham last year, Chelsea were convinced of Cuevas' talent, but were happy to wait until the summer to negotiate a price with O'Higgins. But those plans had to be ripped up as Udinese made a formal approach last month.
Having seen national team stars Alexis Sanchez and Mauricio Isla utilise the Udinese pathway to go onto bigger things at Barcelona and Juventus respectively, Cuevas would've been forgiven if he'd chosen the Italians ahead of Chelsea. But after his trial in London, Cuevas was convinced Chelsea was the best place for his career.
"I approached the week with maturity to keep improving and vowed to try to come back in the future."
It was that desire which allowed Chelsea to knock €1 million off O'Higgins' valuation when serious negotiations kicked off.
Alerted by their South American scout Jorge Alvial of Udinese's move, Chelsea brought forward plans of a summer deal to close an agreement last month. O'Higgins were insisting on €3 million for the 17 year-old, but Chelsea refused to go higher than €2 million. Despite the option to sell to Udinese, O'Higgins agreed to respect Cuevas' wishes and accept Chelsea's final offer.
"Chelsea have been in contact with us for a long time," confirmed Pablo Hoffman, O'Higgins' general manager.
"There is no player like him in Chile. He's left-sided, an attacker, tall, who can score goals."
Perhaps influencing Cuevas' decision-making was Clarence Acuna, the former Newcastle United and Chile midfielder.
Acuna accompanied Cuevas on his trial at Cobham and has been involved in negotiations. After three years in England, Acuna is well placed to advise Cuevas on what to expect from Premier League football.
"It was five days in which I learned a lot and discovered where I can give more," Cuevas recalled, also admitting surprise at how senior players, like Frank Lampard and Fernando Torres, mixed with the juniors.
"We trained with them and I saw that they were good people. You think they would be big headed, but they're nothing like this, they were friendly and even gave advice.
"For me, to be with players who you only see on TV and to be with them on the same pitch, was a dream come true."
With the charm offensive successful, the midfielder will move to London after this summer's U20 World Championships, giving him plenty of time to brush up on his English.
"It will be a big change for me," says the teen.
"It is very different compared to Chile, I realized that when I was there. I've now started going to English classes, I have to learn to communicate well with them.
"But I am calm and happy."