Judge Claudio Bonadio's ruling came after he halted processing the extradition request this week for 30 days in order to seek more information from U.S. justice officials.
Argentine nationals Hugo Jinkis, 70, and his son Mariano, 40, are among corporate executives and former and current FIFA officials indicted on racketeering charges.
"Taking into account the satisfactory way Hugo and Mariano Jinkis have been fulfilling the house arrest conditions imposed on them, it is feasible to reconsider how they wait out this process," Bonadio wrote in separate rulings for each defendant.
Football was thrown into turmoil in May when U.S. authorities accused the Jinkis and 112 others of corruption by taking part in a criminal scheme involving more than $150 million in bribes and kickbacks.
Court documents showed that under new conditions laid out by the judge, neither Jinkis can stay away from his home for more than 24 hours at a time without the permission of the court. Both are forbidden from travelling more than 60 kilometres (37 miles) from the court in the Argentine capital, Buenos Aires.
The passports of the father and son, who are controlling principals of sports marketing business Full Play, will remain confiscated and neither is allowed to travel outside the country.
A third Argentine businessman caught up in the FIFA investigation, Alejandro Burzaco, last month pleaded not guilty in a U.S. court to charges including conspiracy to commit racketeering and conspiracy to commit wire fraud.
(Reporting by Maxilimiano Rizzi; Writing by Richard Lough; Editing by Richard Chang)
