Officers probing the case have found that the pilot Captain Zaharie Ahmad Shah had received a two-minute phone call from an unknown woman, whose mobile number was obtained under a false identity.
The Malaysian jet MH370 had gone missing on March 8 during a flight from Kuala Lumpur to Beijing in China. There were 239 people aboard, most of them from China.
Captain Shah's phone records were checked on Monday for any possible clues that could help solve the mystery of the missing plane, according to News.com.au.
Police are believed to have traced the number to a shop selling SIM cards in Kuala Lumpur, report said.
The SIM card is said to have been bought recently by someone who submitted a woman's id proof to obtain the number.
Meanwhile, the police are reportedly planning on speaking with the pilot's wife following reports about the mystery woman.