"Additional strengthening is forecast during the next 48 hours," the NHC said.
As of 11 a.m. EDT, the storm was located about 510 miles west-northwest of the islands, with maximum sustained winds of 40 mph as it moves west-northwest at 13 mph.
Rene is expected to become a hurricane this week but then weaken over the open waters of the Atlantic, according to the NHC.
Bermuda may need to keep an eye on Tropical Storm Paulette, the second system currently in the Atlantic.
The NHC's advisory at 11 a.m. EDT had the storm with 60 mph winds and located about 1,090 miles east of the Northern Leeward Islands, moving west-northwest at 9 mph.
The storm is forecast to continue moving northwest through Friday night and Saturday.
"Some weakening is forecast during the next couple of days," the NHC said.
Bermuda needs to monitor Paulette early next week for possible impacts, but for now Paulette isn’t expected to strengthen significantly through the weekend. The storm is expected to generate rough surf that will reach the Greater Antilles, Bahamas and Bermuda into the weekend.
Neither of these storms will have a direct impact on the U.S.
Another tropical disturbance southwest of Bermuda has a slight chance of gaining some tropical organization as it approaches the Carolinas by Friday. As of Wednesday, it's not a major concern, as environmental conditions are marginal at best.
A system is moving off Africa in the next couple of days and has the potential to become a tropical depression by the weekend.
Rene was one of two storms that formed Monday; Tropical Storm Paulette took shape earlier in the day in the central Atlantic, far from land.
Historically, September produces the most Atlantic Ocean basin tropical activity. The two current tropical storms are the earliest 16th and 17th named storms, continuing a trend during the 2020 Atlantic hurricane season.
Tropical activity historically climbs through Sept. 10, when it peaks and starts to slowly go back down.
NOAA forecasters are now calling for up to 25 named storms with winds of 39 mph or higher; of those, seven to 10 could become hurricanes. Among those hurricanes, three to six will be major, classified as Category 3, 4 and 5 with winds of 111 mph or higher.
That's far above an average year. Based on 1981-to-2010 data, that is 12 named storms, six hurricanes and three major hurricanes. So far this year, there have been 17 named storms, including five hurricanes.
The 2020 Atlantic hurricane season runs from June 1 to Nov. 30 and includes the names Arthur, Bertha, Cristobal, Dolly, Edouard, Fay, Gonzalo, Hanna, Isaias, Josephine, Kyle, Laura, Marco, Nana, Omar, Paulette, Rene, Sally, Teddy, Vicky and Wilfred.
Fox News' Adam Klotz and Brandon Noriega contributed to this report.