The winner at the 2007 Daytona 500 joined RCR in 2001 and is under contract to Childress through the 2010 season.
The Web site's report said he is trying to move to Stewart-Haas Racing.
Harvick drives the No. 29 Chevrolet Impala SS and has a sponsorship contract with Shell/Pennzoil.
"Richard Childress Racing has a multiyear contract with Shell-Pennzoil that includes the 2010 NASCAR Sprint Cup Series season," RCR said in a statement late Wednesday to the Charlotte Observer. "Shell-Pennzoil remains a great partner for RCR and Kevin Harvick as well as our sport overall."
Harvick has not won a race this season, but was the runner-up at the Daytona 500 in February.
SI.com also said Danica Patrick, one of three women on the IndyCar (IRL) circuit, toured Stewart-Haas Racing's shops in Kannapolis, N.C., on Monday and has definite interest in the organization.