NEW ORLEANS—BP PLC is on track to double the amount of oil collected from a leaking well in the Gulf of Mexico next week, but Tropical Storm Alex threatens to interrupt efforts to contain the spill for up to 14 days, U.S. Coast Guard Admiral Thad Allen said Saturday.

A decision to evacuate would need to be made five days before gale-force winds are expected to reach the spill, where 6,000 vessels and over 38,000 people are involved in the cleanup, Adm. Allen said. The National Hurricane Center said Saturday that the storm...