The jet, which sprung a leak minutes after the launch from Florida on Friday, continued to spew nitrogen tetroxide despite astronauts' efforts to stop it.
The shuttle crew was not in danger, but Russian Space Agency officials said the leak could damage Mir, and a Soyuz capsule docked there, if Discovery approached too close.
"They are busily looking at the situation and hoping for the best in terms of the rendezvous," said Kyle Herring, a National Aeronautics and Space Administration (Nasa) spokesman stationed at the Russian control centre in Kaliningrad, a suburb of Moscow.
Original plans called for Discovery to fly as close as 33ft (10 metres), then back away and circle the space station.
Before the flight, the United States and Russia agreed that the shuttle would stay at a distance of 1,000 feet (300 metres) unless certain that its 44 steering jets were working properly. The leaking thruster is not needed for the rendezvous, but is attached to the same manifold as another jet that is.
The manifold supplies propellant to the steering jets, which often leak when exposed to cold temperatures in space. The astronauts can stop Discovery's leak by shutting down the manifold, but that would put the needed jet out of service.
Mission operations director Randy Stone said he hoped that the shuttle would, at worst, be forced to stay at a distance of 400 feet (120 metres).
Nasa played down the difficulties marring the mission intended as a pathfinder for another shuttle that will dock at Mir in June.
"No matter what we do... we will still be getting a lot of good information for that flight," co-pilot Eileen Collins said in an interview with Cable News Network. Ms Collins, Nasa's first woman shuttle pilot, was assigned to monitor shuttle systems during the rendezvous and was not scheduled to be at the controls.
A second, larger leak erupted in a thruster on Discovery's nose late Saturday, leading to a momentary scare. Jim Wetherbee, Discovery commander, and Ms Collins managed to stop the leak by closing a manifold and firing the jet to blow out an apparent blockage. They tried the same procedure on the aft jet three times yesterday without success. "We show no change in the jet," Nasa Mission Control's Story Musgrave said from Houston.
Ground controllers told the shuttle crew, including the veteran cosmonaut Vladimir Titov, that the leak appeared to be diminishing and they hoped it would "heal itself" in time for the shuttle's appointment today with Mir.