Ms Griner, 31, was convicted in Russian court earlier this month on drug charges and handed a nine-year sentence.
President Joe Biden slammed the verdict, saying that it was “unacceptable”.
The US has put forward an offer to exchange Ms Griner for Russian arms dealer Viktor Bout, who’s serving a 25-year prison sentence in the US.
“I got permission to go to Russia to help that girl,” Mr Rodman told NBC News on Saturday. “I’m trying to go this week.”
It’s unclear who gave him permission.
“It is public information that the administration has made a significant offer to the Russians and anything other than negotiating further through the established channel is likely to complicate and hinder release efforts,” an anonymous senior administration official told Reuters.
The official commented that the State Department is advising Americans to avoid going to Russia.
Mr Rodman has attempted to play a role in international relations previously, being one of few people from the West to have met North Korean leader Kim Jong Un. He’s visited the country several times over the last ten years, NBC noted.
After visiting Moscow in 2014, he said Russian President Vladimir Putin was “cool”.
He also appeared in Singapore in 2018 as then-President Donald Trump attended a summit with Kim Jong-Un there.
Mr Rodman has also claimed that he played a role in getting Kenneth Bae, an American, out of North Korea, according to Time magazine.
Following its invasion of Ukraine, the US has put in place severe sanctions on Russia with the arrest and detention of Ms Griner adding to the tensions.
Former US ambassador to the UN Bill Richardson told the Associated Press earlier this month that he’s optimistic that a swap for Ms Griner and former Marine Paul Whelan can be done in exchange for two Russians.
“I think a two-for-two deal is hopefully a likely outcome,” he said.
“Do not travel to Russia due to the unprovoked and unjustified invasion of Ukraine by Russian military forces, the potential for harassment against US citizens by Russian government security officials, the singling out of US citizens in Russia by Russian government security officials including for detention, the arbitrary enforcement of local law, limited flights into and out of Russia, the Embassy’s limited ability to assist US citizens in Russia, COVID-19-related restrictions, and terrorism,” the state department says in its advisory. “US citizens residing or travelling in Russia should depart Russia immediately. Exercise increased caution due to wrongful detentions.”
Mr Rodman spoke to NBC in a Washington, DC restaurant. He was visiting the capital to attend a sneaker convention.
“I know Putin too well,” he told the outlet.