The club have been chasing Montero for some time and are ready to make a move for him this summer, with the player keen to make a switch away from Mexico.
"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," Montero said.
Gary Monk will need to add to his attacking options ahead of the new season with Wilfried Bony and Michu both likely to depart this summer.
The Swans have already been linked with a move for Marseille winger Dimitri Payet as well, so it would appear that Garry Monk is hoping to strengthen the wide areas.
Montero has also been linked with a move to rivals Cardiff City and West Ham as well so Swansea will need to act fast if they are to sign the tricky left-winger.
The former Villarreal man impressed at the World Cup this summer despite the fact that Ecuador failed to progress through the group stages, and interest in the 24-year-old will only heighten as a result.
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He wasn't able to get a goal during the tournament but enjoyed an average of 42 touches per game - more than Manchester United winger Antonio Valencia, and was always a threat for his side.
Swansea look to be closing in on the signing of Montero and for just £4 million, they will be able to continue to invest in the squad ahead of the new campaign.
Would Montero be a good signing for Swansea?