24-year-old Javary has been looking to move to England from Scottish First Division side Raith Rovers for some time, and recently spent time at Valley Parade on trial with Bradford.
The former Brentford and Plymouth player has now arrived in South Yorkshire in search of a move to The Blades, and he did his chances no harm when impressing in United's reserves game against Tranmere, when he scored the team's only goal in a 3-1 defeat.
While Warnock mulls over a move for Javary, he also had a look at Blackburn's Scottish defender MacNamee, who played at right back in the reserves. He also played well but it looks like Javary could be the man handed any deal with the club.
One man who has signed a deal is defender Rob Ullathorne, after he had been playing on a non-contract basis since Christmas.
The 30-year-old former Norwich and Leicester City player has signed until the end of next season, but Warnock says that he could well be offered a longer deal if he continues to perform well.
"It's a good move for both Rob and the club and I'm happy have to tidied up the situation," Warnock told the club's website.
"He's a consistent and reliable player to have and, since coming back into the side, he has staked a real claim for his shirt."
After a lengthy time out with injury, Ullathorne has secured his place in the side at left back, and played his 11th game in a row in Wednesday's 1-0 defeat at Coventry, earning high praise from the manager.
"We think he's done ever so well," Warnock told BBC Radio.
"He turned down more money than I've given him now six months ago, because his agent told him that he'd get double in Spain.
"We'll talk in October or November about extending it."
Meanwhile, Argentinian trialists Juan Manuel Martinez and Ezequiel Iglesias have left the club after completing their temporary stay at Bramall Lane.
Warnock was impressed with both of the South Americans, and was hoping to hang onto them for a further month, but the duo were looking for a permanent offer, and have moved to Holland to try and get a deal there.
