Montero has been a long-term target for Swansea and they are keen to bring him to the Liberty Stadium this summer.
The 24-year-old impressed during the World Cup with Ecuador despite the South Americans failing to get beyond the group stages.
Montero recently admitted he was hoping to win a move to Europe from Mexican side Monarcas Morelia this summer with a number of clubs chasing his signature.
"The club are handling it. Let’s see where I’ll go but for now I have some days off," said Montero.
"It’s certain that I’ll leave the (Mexican) league, but let’s see where I’ll go. We expect to sort it out within the next few days. It will be Europe and thank God we are working on it, I hope it works out."
Swansea are hoping to win the race for the skilful wide-man as Garry Monk looks to add to his attacking options ahead of next season.