Sergei Bout said Viktor Bout's defense team had not been notified of the attempt.
Viktor Bout, 41, was arrested in March in a joint police operation led by the U.S. Washington is seeking Bout's extradition on charges of illegal weapons deals with militant groups, including the Taliban and al-Qaeda, in Middle East and African countries.
His arrest came as part of a sting operation involving a 'deal' to sell and deliver surface-to-air missiles, helicopters and rocket launchers to the Revolutionary Armed Forces of Colombia (FARC). The group is listed as a terrorist organization in the U.S.
Thai authorities said on Wednesday that they would not bring charges against Bout, but would keep him in custody pending a decision on a U.S. extradition request.
Washington has not yet filed the request and has 60 days to do so. Bout could face 15 years behind bars if found guilty on the U.S. charges.
Russia's Foreign Ministry said on Thursday it would monitor the investigation by Thai police and look into the legitimacy of the accusations against Bout, adding that the suspected arms dealer did not face any charges in Russia so there were no grounds to extradite him to the country.
Bout is a former lieutenant in the Russian military who quit the armed forces in 1991. He then allegedly transformed himself into an international arms dealer, earning the nickname 'the Merchant of Death.' Western media has consistently referred to him as a "former KGB officer."
Western law enforcement agencies consider him to be "the most prominent foreign businessman" involved in trafficking arms to UN-embargoed destinations.
U.N. reports say Bout set up a network of more than 50 cargo aircraft around the world to facilitate his arms shipments.
U.S. authorities took measures against Bout in 2005, freezing his bank accounts and submitting a list of 30 companies linked to Bout to the UN Security Council Sanctions Committee.