People across Florida were given notice Sunday that Milton, for now just a tropical storm off the coast of Mexico, could intensify rapidly into a major hurricane before slamming midweek into the storm-ravaged Gulf Coast.

Tropical Storm Milton’s center was about 860 miles (1,385 kilometers) west-southwest of Tampa, Florida, early Sunday, heading east at 5 mph (7 kph) with maximum sustained winds of 60 mph (95 kph), the National Hurricane Center in Miami said.

“Milton is moving slowly but is expected to strengthen rapidly,” the center said. “There is increasing confidence that a powerful hurricane with life-threatening hazards will be affecting portions of the Florida west coast around the middle of this week.”