Divers in the lake, and (inset) some of the relics
The theory arose following the discovery of a 2,500-year-old ancient world settlement submerged 23 metres under the second biggest saline lake in the world.
At the site, in the waters of lake Issyk-Kul, in eastern Kyrgyzstan, Russia, the discovery a piece of a large "unique" ceramic pot found with a stamp written in Armenian and Syrian scripts among 200 relics, also supports the theory, researchers claim.
lake Issyk-Kul is the tenth biggest lake in the world and second only to the Caspian sea in terms of saline lakes.
If confirmed as suspected, the discoveries support the belief that St Matthew's relics and remains were buried on the site that is thought to have gone on to become an Armenian monastery in Medieval times.
The water is the second biggest saline lake in the world
Dmitry Gorn, director of Tomsk scuba diving, who led the diving team, described the inscribed pot fragment as "truly unique" and said experts were working to identify of the writings, believed to be Armenian-Syrian script.
He said: "If that proves to be correct, it will be further evidence that there was an Armenian monastery on Issyk-Kul in the 14th century where, according to the legends, relics of Matthew were stored."
Many Christians believe Matthew the Apostle's remains are in Salerno Cathedral, Italy, - a building dedicated to the saint.
The inscriptions on the inside of the large pot
But the Orthdox Church is not convinced by this, believing he is at Issyk-Kul.
Its followers claim St Matthew's was killed in Syria, and his followers escaping from the Romans, hid his body before burying it on the beach of Issyk-Kul.
Dr Vladimir Ploskikh, of the department of history and culture at the Kyrgyz-Russian University, said: "His followers, escaping from Rome's persecutions, brought the relics of the Apostle to this land."
Divers worked in Tup Bay, in the northeast of the lake,
Mr Gorn said: "The underwater archeological expedition allowed us to find a previously unknown Saka settlement with evident signs of bronze casting production on the bottom of Lake Issyk-Kul.
More of the 200 relics found in the lake
Dozens of artifacts were raised from the lake.
He added: "We lifted over 200 items among them mainly pieces of ceramics, whetstones for sharpening knives, a piece of bronze ritual sickle, and many pieces of slag and traces of casting production."
It is the latest in a number of ancient sites under the water.
In 2007, Dr Ploskikh, vice president of the Kyrgyz Academy of Sciences, revealed archaeologists found remains of a 2500-year-old advanced civilisation there, including
bronze battleaxes, arrowheads, daggers, a gold bar, ancient coins and burial mounds of the Scythian people.