The 32-year-old Spaniard had ankle surgery at the start of February and was expected to be sidelined for two months.
Leeds have failed to score in five of their last seven matches and the possible return of Rodrigo, and forward Luis Sinisterra, would be a timely boost to their top-flight survival bid.
Boss Javi Gracia said: “They are doing something with the team. Some long-term injured players need a process to adapt, to come back with the team, but they are doing some (training).
“The next training session (on Friday) we will evaluate the situation they are in. Can they help us in the next game, or is it better to wait?”
Leeds have won only one of their last 12 league games and sit one point above the relegation zone.
Rodrigo, Leeds’ top scorer this season with 12 goals in 22 appearances in all competitions, injured his ankle in an FA Cup win at Accrington at the end of January.
Sinisterra has been out since pulling a muscle in Leeds’ 2-2 Premier League draw at Manchester United earlier this month and had been hopeful of returning in time for last week’s 1-0 defeat at Chelsea.
Gracia will take charge of his fourth game against high-flying Brighton since replacing Jesse Marsch last month.
The former Watford boss made an encouraging start as a home win against Southampton lifted Leeds out of the bottom three and he has called on the Elland Road faithful to once again play their part.
“It’s crucial for us,” Gracia said. “We know first of all, playing with our supporters is always better. They helped us in the last home game.
“In my opinion they were the difference for us to be able to win the game and I expect the same for the next game, playing home and playing away because when we play away you can see 7,000 people supporting you.
“I want to thank them because they are supporting a lot and we can feel it. It’s true in the last home game against Southampton, the atmosphere was unbelievable and it was what we needed to get the good result.”
Gracia confirmed Chris Armas has left the club just weeks after joining up with predecessor Marsch’s backroom staff.
Following Gracia’s arrival, Leeds confirmed he had been joined by assistants Zigor Aranalde and Mikel Antia, plus conditioning coach Juan Sollas.
Under-21 boss Michael Skubala, who had a three-game spell as interim boss, has since been promoted to the first-team coaching staff.
Forward Patrick Bamford is hoping to return to contention after missing out at Chelsea due to a knock, while defender Liam Cooper remains doubtful after missing the last six games due to a muscle strain.