The News of the World says the Real America midfielder may not be well known in England but David Moyes's scouts have been impressed by his performances for Bolivia's Under-20 national team.
Galindo will come relatively cheaply at around £750,000 which would be within Moyes's tight budget at Goodison Park.
"I have all my paperwork in order to travel to England," he said. "First, I will undergo the medical examination and then proceed to the contract signing so I'm travelling with my dad."
The 17-year-old has previously been linked with Wigan but Moyes appears to have won the race to sign him.
"I hope not to waste this opportunity to prove to everyone that there are good players in Bolivia," he added.