Saif al-Islam al-Qadhafi, who runs the Qadhafi International Association for Charitable Organisations and who has assumed an increasingly prominent international role, said on Monday that Libya would also soon open its embassy in the American capital.
"The Libyan and American flags will be raised in Tripoli and Washington within the coming days," he said.
There was no immediate confirmation from the US State Department.
Al-Qadhafi said American and Libyan officials were negotiating the embassy reopening in the Libyan capital and removal of the Libyan government from the list of countries sponsoring terrorist acts.
He was speaking a day after visiting Senator Richard Lugar, the Republican chairman of the Senate Foreign Relations Committee.
Libya has been on the State Department-compiled list since 1979.
"The Libyan and American flags will be raised in Tripoli and Washington within the coming days"
Saif al-Islam al-Qadhafi
Al-Qadhafi junior said he hoped to visit the United States and exhibit his art work there.
He currently has exhibitions in a number of countries in Europe and the Middle East.
Relations between Washington and Tripoli, strained since the senior al-Qadhafi came to power in a military coup in 1969, have steadily improved during the past year.
In June 2004, the United States opened a liaison office in Tripoli, 24 years after Washington closed its embassy in the North African country.
Last year, the United States took steps towards normalising trade and investment relations with Libya, including the import of Libyan oil.
Better relations were based largely on the Libyan leader's decision to give up the pursuit of nuclear weapons and financial settlements with the families of the victims of the 1988 Pan Am 103 bombing over Lockerbie, Scotland, in which 270 people - most of them Americans - died.
Libya wants Washington to remove sanctions, in place since 1986, that are estimated to have cost the country more than $30 billion in lost business.
The removal of the sanctions is expected to accelerate US investment in Libya's oil industry, the country's main source of revenue.
In another sign of an improved image for Tripoli, the new King Abdullah of Saudi Arabia pardoned Libyans earlier this month for their alleged involvement in a plot to assassinate him when he was crown prince.
On that matter, al-Qadhafi junior said: "We consider that this page has been closed.
"We shouldn't dig up the past. We look forward to the resumption of relations [with Saudi Arabia] soon."