Muhammad al-Gharabawi, in his 50s, was captured while delivering petrol products to US forces in Iraq by a group that it said represented the "legitimate Iraqi resistance", Aljazeera reported last week.
Faisal al-Nahait, who owns the transport firm where al-Gharabawi had worked for eight years, said unidentified callers had telephoned him several times since Wednesday demanding money. He urged Egyptian authorities to help secure the driver's freedom.
"The last call was on Friday evening and the caller demanded $1 million. I told him I am ready to help free a fellow Muslim but I cannot pay that kind of money," al-Nahait said from northern Saudi Arabia.
Al-Nahait, a subcontractor who had been delivering Saudi fuel supplies to Iraq for nearly a month, denied his company was working with US forces there. He said his company was one of dozens of Saudi subcontractors delivering fuel under a contract with the Iraqi government.
He said he had told the Egyptian embassy in Riyadh of the telephone calls, but no one had contacted him.
"It is important that Egyptian authorities help secure al-Gharabawi's release," he said.
Al-Nahait said three oil lorries went missing last Saturday, along with their drivers. Two Pakistani drivers, who had said they were kidnapped and robbed of their personal belongings, had since returned to Saudi Arabia, he said.
"I doubt that those people are Iraqi resistance. They sound more like thieves," he said.
Dozens of foreigners have been seized in Iraq since April. At least four have been killed, including an American and a South Korean beheaded by the Jamaat al-Tawhid and Jihad group led by al-Qaida ally Abu Musab al-Zarqawi.