The National Hurricane centre says Rosa is strengthening and is forecast to become a major hurricane later today or tonight.
Rosa is expected to hit Baja California in Mexico and its effects could be felt on the US Pacific coast.
It is currently tracking the Pacific Ocean and is heading west at 10mph (17km/h).
The storm will be accompanied by a barrage of strong winds and torrential rainfall.
It is currently rated as a Category 1 storm, with winds currently clocking 86mph.
According to the Saffir-Simpson scale, a category one hurricane has "very dangerous winds" which "will produce some damage".
NOAA have placed Rosa 630 miles west-southwest of Puerto Vallarta, Mexico and 485 miles southwest of the southern tip of Baja California, Mexico.
Rosa is now the tenth hurricane of the Pacific hurricane season which lasts for around six months.
AccuWeather Senior Meteorologist Dan Pydynowski said: "The track of Rosa will keep it well west of Mexico through the weekend, meaning the primary impact to land through the weekend will be limited to rough surf and rip currents along the western coast of Mexico."
"Regardless of its exact intensity as it approaches the Baja, moisture from Rosa will be pulled northward and northeastward across northern Mexico and into the southwestern United States.
"This could lead to locally heavy rainfall and flash flooding later next week across parts of the southwestern U.S."
At least 18 people were killed after heavy rainfall from Hurricane Florence hit the Atlantic coast earlier this month.