It had been thought that the Londoners had offered around £2.2million, with Cuevas' club, O'Higgins, hoping to hold out for at least £3.4million.
The left midfielder has played for Chile Under-20s, and could be moving to Stamford Bridge in the summer if everything goes to plan, says the Daily Mail.
Cuevas' agent, Mauricio Valenzuela, believes the deal is close to being done: "The negotiations are very advanced with Chelsea.
"There are still a few details, but the situation is very advanced.
"We have been working on this for a while, the idea is that players can leave Chile and be successful.
"Chelsea have been following him for a couple of years, and the offer was made due to his good performances'"