Karime Macias Duarte, 43, is expected to avoid prosecution for alleged fraud totalling 4.9 million USD over the UK’s failure to extradite her.
Ms Duarte is the subject of an Interpol red notice after Mexico issued an arrest warrant last October, and her extradition has been sought since then.
However, she may avoid prosecution as the statute of limitations on her alleged fraud will run out next year.
The Home Office refused to confirm whether the extradition request had been approved, The Times reported.
It comes as Dominic Raab, the foreign secretary, prepared to travel to Mexico City amid the UK’s promise to invest £60m over the next five years to fight poverty and corruption in Mexico.
Thousands of people disappeared between 2010 and 2016, when he was governor, and hundreds of bodies have been found in mass graves.
His administration was also accused of watering down medicines for child cancer patients.
His wife, also known as Karime Tubilla, is believed to have fled to London as her husband vanished in a government helicopter, before he was arrested in Guatemala in April 2017and extradited back to Mexico.
She is seeking asylum in Britain, according to reports in Mexico, so the request for her extradition could be held up in the courts for years.
When he gave an interview from jail earlier this year, Duarte said his family was living “in austerity” in London and claimed his wife was a “victim of political persecution”.
However, Veracruz officials said they had footage of her living in central London and shopping at expensive stores.
She was also said to have sent her three children to a private school.
Authorities in Mexico allege she wrote the phrase “I deserve abundance” 45 times on a single page in her diary.