Richardson has visited North Korea on two previous occasions in the 1990s and convinced Pyongyang to free US prisoners.
He has also held talks before in Santa Fe with North Korean diplomats to the UN - in 2004 and 2006.
Clinton 'private' talks
The meeting with the two representatives this week will conclude with discussions on renewable energy technology that are being developed in New Mexico, a statement from the governor's office said.
The talks in Santa Fe come a day after Bill Clinton, a former US president, briefed Obama on his visit to Pyongyang, where he met Kim Jong-il, the North Korean leader.
Two US journalists who had been jailed by North Korean authorities for spying were released shortly after Clinton concluded his visit last month.
The White House has insisted Clinton visited the North Korean capital in a private capacity and has denied that he delivered any message from Obama.
The meeting between Clinton and the North Korean leader marked the highest-level US contact with North Korean officials since the country opted out of six-party talks that included the US and South Korea on its nuclear programme.
Since leaving the negotiations, Pyongyang has tested a long-range missile and held nuclear weapons tests.