The four-time Olympic champion, 39, revealed in the BBC documentary The Real Mo Farah how he was brought to Britain from Somalia illegally having assumed the name of another child after his father was killed in the civil war.
His real name is Hussein Abdi Kahin but he will continue to go by Mo Farah.
In a statement on the revelation, the Met Police said: “We are aware of reports in the media concerning Sir Mo Farah. No reports have been made to the MPS (Metropolitan Police Service) at this time.