The vessel belongs to the Libyan government's shipping arm, the General National Maritime Transport Company, which is believed to be controlled by Gaddafi's son Hannibal, who is on a sanctions list.
The source said the tanker then set a course for Benghazi and was being shadowed by NATO, which has 17 ships in the Mediterranean enforcing a U.N. arms embargo on Libya.
NATO confirmed it was tracking a tanker but said it had no information to confirm that the Cartagena had been seized.
"We are monitoring the ship and the ship has been hailed and signs indicate it is cooperating with NATO forces as it approaches the shores of Libya," NATO spokesman military Colonel Roland Lavoie said.
"NATO will follow normal procedures and it will be up to commander of the NATO ship involved to decide whether to board the ship, weather and sea conditions permitting."
Lavoie said he had no information as to the specific whereabouts of the ship.
A petroleum industry newsletter said the Cartagena was seized by anti-Gaddafi rebels with the help of special forces from a European state.
The Petroleum Economist said on its website that the tanker had been boarded by Libyan nationals acting without the knowledge of the rebel National Transitional Council based in Benghazi.
It quoted "a source familiar with the operation" as saying a European government had lent logistical support to the operation, which it said was believed to have involved special forces boarding the ship from the air.
Lavoie said NATO was aware of the report but "was not in a position to speculate" about its veracity.
A trader with a major oil firm told Reuters he had learned that the Cartagena, carrying a cargo of gasoline, had been hijacked by the rebels, but gave no further details.
The Petroleum Economist said the Cartagena was carrying almost 40,000 tonnes of gasoline. It said the ship was originally chartered to land the fuel in Tripoli and had been stranded in the Mediterranean after NATO began intercepting seaborne fuel supplies for Gaddafi in May.
Rebels fighting Gaddafi also seized a Libyan state-owned gasoline tanker carrying gasoline to Libya for the National Oil Corporation in March.
While not specifically charged with enforcing a fuel embargo on Libya under the terms of its U.N. mandate, NATO said in May it had intercepted an oil tanker which it said it had reason to believe was set to deliver fuel to Gaddafi's forces.
It said then it would continue to do so on a case-by-case basis.