It quoted Deputy Prime Minister Igor Sechin as saying that Hayward "is leaving his post." Sechin, who is set to meet with Hayward on Monday, said the BP chief would introduce his successor.
A spokesperson at BP's headquarters in London told CBS News Monday, "categorically, Tony Hayward isn't resigning."
The company official said Hayward "remains BP chief executive." The official said the energy company was trying to determine where Sechin got his information.
Hayward was to assure officials of BP's viability and discuss issues related to Russian joint venture TNK-BP, which accounts for about a quarter of BP's reserves and production.
It's not the first time BP has had to quash reports that its senior executive was stepping down in the wake of the disastrous oil spill.
The report out of Russia comes exactly one week after BP's headquarterscirculating in the Gulf region that Hayward would step down following an attack on his character by U.S. lawmakers.
Hayward came under intense pressure to step aside, most recently from Sen. Richard Shelby, R-Ala., who said a week ago on CBS' "Face the Nation" that the oil company boss "should go".
Shelby said the fact thatreflected his "gall" and "arrogance," and illustrated why he should not be in charge of the company.
"I thought that was the height, height of stupidity, and I believe myself that he should go," Shelby told Bob Schieffer. "I don't know how he can represent a company in crisis like BP and ignore what's going on in the Gulf of Mexico."
Hayward hasinvolving the oil spill cleanup in the Gulf to Bob Dudley, a BP managing director who has helped manage the company's on-the-ground response since May.