The 24-year-old took up an invitation to travel to Thorp Arch at the start of the month and he appears to have persuaded Leeds to add him to their squad after securing an extended chance to impress manager Simon Grayson.
Grayson fielded Nunez in a reserve team match at Bradford Park Avenue a little over a fortnight ago and also watched him in a behind-closed-doors friendly at Thorp Arch last week.
Nunez requires a work permit to play in the Football League but the attacking midfielder is a regular member of Honduras' international squad and an application to the Home Office would be unlikely to meet any obstacles.
Leeds may also look to extend Adam Clayton's time at Elland Road following the expiry of his loan from Manchester City.
Clayton was signed by Grayson on a month-long deal and United's first-team fixture at Vicarage Road on Saturday was the last of his initial spell in Yorkshire.
The 21-year-old has made two appearances as a substitute for Leeds but is unlikely to play any serious part in a large and expensively assembled squad at Eastlands.
Grayson hinted over the weekend that further deals would develop in the hours before tomorrow's transfer deadline, and a defensive midfielder is still believed to be high on his list of priorities to bolster United's squad.
Leeds, however, are not expected to follow up their interest in Cardiff City's Gavin Rae.