The National Hurricane Centre's forecast on Monday morning put Ernesto's track almost directly over Kennedy Space Centre for late Wednesday or early Thursday, and listed a nearly 50 per cent chance of tropical storm force winds.
If Nasa does decides to move Atlantis, it will not start until Tuesday, allowing engineers a chance to launch on September 3 if Ernesto's track moves away from Florida, a spokesman said on Monday.
Nasa is keeping an eye on tropical storm Ernesto, which forecasts show could regain hurricane strength before striking western Florida later this week.
Weather-related events have frustrated Nasa's attempts to launch its first International Space Station construction mission in nearly four years.
The shuttle has been cleared of any damage after a lightning strike on Friday.
Ideally, Nasa wants to lift off by September 7 to avoid any conflict with a Russian Soyuz rocket mission.
Once it launches, Atlantis will carry six astronauts and a 16-tonne segment with two huge solar panels for the half-finished space station.
It would be the first of 16 flights planned to complete assembly of the space station by 2010, when the shuttle fleet is set to retire.
The Atlantis mission will be the third shuttle flight since Columbia blew up after its heatshield, which was damaged by falling debris on lift-off, failed on re-entry.
After two Discovery shuttle flights in the past two years aimed at improving safety, Nasa said it was ready to resume construction of the station, which is key to US plans to send humans to Mars.
The installation of the solar panels will provide a quarter of the station's power and is one of the most complex parts of the assembly sequence.
Three spacewalks are planned during the 11-day Atlantis mission, which will be followed by another shuttle flight planned for December.