Although the judge who led a six-month inquest into the death of Princess Diana and boyfriend Dodi Fayed decided against asking for a police investigation of Burrell, the force said an unidentified person had filed a complaint.
"In view of the complaint received, the Metropolitan Police Service has a duty to look at whether Paul Burrell should be considered for perjury," said a spokesman, speaking on condition of anonymity in line with department policy.
"In considering this matter, we will of course take note of the coroner's decision not to refer this matter to us."
Confirmation of the complaint emerged hours after Fayed's father, Mohamed Al Fayed, announced that he was ending his long and costly campaign to prove his belief that the couple were murdered by British secret agents.
The couple, along with their driver, died in a car crash in Paris in 1997.
"I'm a father who has lost his son and I've done everything for 10 years. But now with the verdict I accept it, but with reservations," Al Fayed said in an interview with ITV.
"But I have (had) enough. I'm leaving the rest for God to get my revenge," Al Fayed said. "I'm not doing anything anymore ... this is the end."
Burrell, who has written two books about his years with Diana, spent three uncomfortable days on the witness stand at the inquest.
After returning to the United States, he was caught on a hidden camera saying he had not told the whole truth during his testimony at the inquest. "I was very naughty, and I laid a couple of red herrings," he was heard to say.
The coroner was scathing in his assessment of Burrell's testimony.
Burrell had refused to return to London to explain himself to the inquest, but he sent a written statement denying that he had lied in his testimony.
"At the time of the secretly recorded conversation, I was tired, depressed and had been drinking all evening," Burrell said.
"During the course of the conversation ... I was showing off. I am not proud of this," Burrell added.