A senior Greek security source said the two Iraq-born British nationals, both in their 20s, were arrested on Saturday night by coastguard officers in the port city of Alexandroupolis.
They were said to be driving a trailer and carrying more than a dozen guns and 20,000 bullets.
A police official said: “We don’t have any evidence to connect them with ISIS.”
The weapons were not combat rifles but could have been used for training, the official added.
Greek police counter-terrorism officers and National Intelligence Agency staff were dispatched to Alexandroupolis, in the north east of the country.
Acting on a tip-off, the Greek police and coast guard set up a surveillance operation over several days which led to the arrest of the two British nationals at the entrance to the port.
They were driving a car towing a caravan. Concealed inside it, police found 18 shotguns, 27,250 22mm bullets, 12,500 5.5mm bullets, currencies including Turkish lira and Iraqi dinars, and seven mobile phones. Another man, a British resident, was arrested near the Kipoi border point on the Evros river, as he was driving a trailer with German number plates.
Inside, police found four Walther handguns, 200,000 22mm bullets, eight pairs of night-vision goggles and cash in various currencies.
The Foreign Office said it was investigating the reports.
A spokesman said: “We are urgently looking into reports that two British nationals have been detained in Greece.”
Yesterday Dutch foreign minister Bert Koenders urged EU member states not to close their borders to migrants, suggesting that “effective border control is more important”.
Mr Koenders, whose country holds the rotating six-month EU presidency, said in the Macedonian capital Skopje that the Netherlands will continue to talk with Austria, Macedonia and Greece to find an effective solution on migrants and avoid unilateral measures.
He said he thinks it is still possible to avoid a “domino effect and an uncontrollable situation”. He also pointed out the need for EU countries to take special care for vulnerable groups of migrants, such as women and children.
Mr Koenders was in the border town of Gevgelija and was to meet Greek Prime Minister Alexis Tsipras.