Sam Allardyce is considering offering contracts to David Carney and Juca, after the unattached pair were given trials by the West Ham boss.
Australian winger Carney, 27, has been training with the east London club having been released by Blackpool at the end of the last campaign.
Juca, meanwhile, is an experienced defensive midfielder, and the 31-year-old is available on a free transfer having left Spanish outfit Deportivo La Coruna.
Both players were handed opportunities to prove themselves on Monday as the Hammers' development squad took on a Tottenham XI in a behind closed doors friendly.
Carney and Juca each played a full 90 minutes as Spurs Lodge in an encounter which ended 2-2, with Frederic Piquionne scoring both goals for West Ham.
Also featuring for the Hammers were summer signings John Carew, Abdoulaye Faye and Papa Bouba Diop, while academy graduate Freddie Sears also got some minutes under his belt.