If bad weather over the Caribbean strengthens and then moves to the site in the Gulf of Mexico, ships will have to be withdrawn.
It could mean no work on the relief well for up to two weeks.
A final piece of casing needs to be cemented in place at the bottom of the relief well before it can then drill into the damaged well.
Once the casing is in place, engineers could begin the last drilling within five to seven days and then "kill" the well with mud and cement.
There is a 60% chance that a weather pattern currently over the island of Hispaniola will turn into a cyclone within the next 48 hours, the National Hurricane Center says. It is currently moving west-northwest.
A reconnaissance flight is to be carried out on Thursday.
Senior BP executive Kent Wells said the relief well currently had a plug in it below the surface in anticipation of bad weather.
If the weather holds, a "static" kill - pumping mud into the top of the well through the new cap - could be done as an intermediate measure. BP and government experts are deciding whether this will take place.
BP would need a weather window of two to four days to place the final bit of casing, cement it and then carry out the static kill operation, Mr Wells said.
The cap applied last Thursday stopped oil leaking from the well for the first time since the explosion aboard the Deepwater Horizon drilling rig on 20 April.