US officials acknowledged at the time that he was removed in error.
In June he was returned to the US, where he was detained and charged with human smuggling. He pleaded not guilty.
Trump officials claim that he is a member of the MS-13 gang, an accusation he also denies.
His deportation case has become a focal point in the administration's crackdown on immigration. Mr Ábrego García has no connection to Eswatini, which is the fourth country floated as a potential deportation destination for him.
Previously known as Swaziland, Eswatini is surrounded by South Africa and Mozambique. It is one of the last remaining absolute monarchies in the world, and has been led by King Mswati III since 1986.
The US has already deported five people to Eswatini, describing them as "criminal illegal aliens" to the country.
The move sparked concern in the small nation that it was becoming a dumping ground for criminals.
Eswatini has not confirmed whether it receives payments for the deportation deal struck with the Trump administration.
The US is the fourth-largest market for the country's biggest export, sugar. Analysts suggest that Eswatini may be trying to safeguard this trade and avoid tariffs.
Mr Ábrego García entered the US illegally as a teenager from El Salvador. In 2019, he was arrested with three other men in Maryland and detained by federal immigration authorities.