Paraguayans Nelson Amarilla and Juan Aguilar are set to win West Ham United contracts after successful trials.
The Daily Mail says Amarilla, 20, a defender, and Juan Aguilar, 19, a midfielder, play for Guarani in Paraguay but have had a week of training in east London.
West Ham manager Gianfranco Zola said the club had yet to make a decision but he thought the Hammers would want them both to stay.
Zola said: "The project is to make a team capable of a high level. We cannot compete by spending £200million so we have to do it through getting young players.
"Not all the time we will be looking abroad. We have good young English players here like Freddie Sears and Mark Noble and we are trying to improve them."