Landing was initially set for Wednesday, but the US space agency rescheduled for a day earlier fearing that its control centre in Houston, Texas may have to be evacuated if it is grazed by Hurricane Dean which is now roaring across the Caribbean.
The hurricane, on track to strike Mexico early Tuesday but missing Texas altogether, "poses little hazard or little risk to the Johnson Space Center mission control area," NASA said in a statement.
Nevertheless, it added: "mission managers continue to monitor Hurricane Dean as it moves westward".
Endeavour is to land at the Kennedy Space Center in Cape Canaveral, Florida, which is not as well equipped as Houston for ground control operations, in the event the Johnson Space Center has to be shut down if the hurricane strikes.
The Endeavour crew will have two chances to land at either 12:32 pm (16:32 GMT) and 2:06 pm (18:06 GMT), NASA said.
The weather forecast for Tuesday at the Cape was relatively dry with any possible showers "probably not expected to be a concern ... so the weather looks good" for a landing, said NASA spokesman Mike Curie in Houston.
Should landing here be called off, the shuttle would try again on Wednesday first at Cape Canaveral, or Edwards Air Force Base in California, or possibly even at the White Sands Space Harbor in New Mexico.
The Endeavour and ISS crews finished a shortened, fourth spacewalk on Sunday, before the shuttle with its crew of seven undocked from the ISS without performing the usual fly-past of the station to take pictures.
"They didn't do a flight around the ISS because it was a very busy day for the crew, undocking and doing the late inspection, all of this in one day," Mr Curie said.
The crew last week put out a robotic arm with a high-definition camera with attached laser to inspect the heat shield on Endeavour's nose and wings for possible damage from meteors and other floating space debris.
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