The call from co-pilot Fariq Abdul Hamid's phone, however, ended abruptly, but not before contact was established with a telecommunications sub-station in Penang state, the New Straits Times reported today.
The call was made as the jet was flying low near Penang island on Malaysia's west coast, the morning it went missing.
"The telco's (telecommunications company's) tower established the call that he was trying to make. On why the call was cut off, it was likely because the aircraft was fast moving away from the tower and had not come under the coverage of the next one," the paper said, citing unnamed sources.
The paper said it was unable to ascertain who Fariq was trying to call as sources chose not to divulge details of the investigation. The links that police are trying to establish are also unclear, said the report.
Investigators are poring over this discovery as they try to piece together what had happened moments before the Boeing 777 Flight MH370 went off the radar, some 200 nautical miles northwest of Penang, the paper said.
Fariq's last communication through the WhatsApp Messenger application was about 11.30pm on March 7, just before he boarded the jet for his six-hour flight to Beijing.
The Beijing-bound Malaysia Airlines flight MH370 - carrying 239 people, including five Indians, an Indo-Canadian and 154 Chinese nationals - had mysteriously vanished on March 8 after taking off from Kuala Lumpur.
The paper said checks on Fariq's phone history showed the last person he spoke to was "one of his regular contacts (a number that frequently appears on his outgoing phone logs)".
This call was made no more than two hours before the flight took off from Kuala Lumpur International Airport.
Citing sources close to the investigations, the paper said that checks on Fariq's phone showed that connection to the phone had been "detached" before the plane took off.
"This is usually the result of the phone being switched off. At one point, however, when the airplane was airborne, between waypoint Igari and the spot near Penang (just before it went missing from radar), the line was 'reattached'.
"A 'reattachment' does not necessarily mean that a call was made. It can also be the result of the phone being switched on again," the sources said.
Fariq and Captain Zaharie Ahmad Shah have come under intense scrutiny after the plane mysteriously vanished.
Investigators last month indicated that the flight was deliberately diverted and its communication systems manually switched off as it was leaving Malaysian airspace.
The probe into the missing plane have been focused on four possible areas - hijack, sabotage, as well as personal and psychological problems.
The FBI has been assisting police, including sharing intelligence and expertise.
Police have not cleared the 227 passengers of the flight MH370 of possible foul play. Clearance has also not been given to the crew.
The mystery of the missing plane continued to baffle aviation and security authorities who have so far not succeeded in tracking the aircraft despite deploying hi-tech radar and other gadgets even after searching for 36 days.