Hutch, who is a nephew of suspected armed robbery mastermind Gerry 'The Monk' Hutch, is understood to be abroad but is likely to be arrested as soon as he comes back to Ireland.
It is claimed that Hutch and Thompson lived together in Spain and were "right-hand men" of Daniel Kinahan -- the son of Ireland's richest drugs trafficker Christy Kinahan.
Like Thompson, Gary Hutch from Sherrard Street in the north inner city is extremely well known to gardai and has a number of previous convictions.
He has previously served jail sentences totalling 10 years for the armed robbery of jewellery worth IR£32,000 and IR£5,000 cash from a businessman, as well as the theft of a motorbike.
Spanish authorities allege that Thompson and Hutch operated as bodyguards and chauffeurs for the Christy Kinahan drugs organisation that was targeted in a massive international police operation in May, 2010, known as Operation Shovel.
Spanish authorities say that the Kinahan drugs organisation is heavily involved in gun crime, drug trafficking and money laundering through a complex network of companies.
Daniel Kinahan was one of around 30 people arrested by police as part of Operation Shovel and Spanish police claim that 'Fat' Freddie Thompson and Daniel Kinahan had a very close personal relationship and that one of Thompson's key jobs was to obtain weapons for the Kinahan drugs organisation.
Sources say that Thompson "laughed and joked" after he was arrested at his home on Loreto Road in the south inner city shortly before 3pm yesterday but that he is "deeply concerned" for his own safety in jail.
"He was mouthing away as usual but you could see that he was a bit worried about going into prison," said a source.
It is understood that prison authorities decided that 'Fat' Freddie should be put in the D2 protection unit in Cloverhill because of fears that the gang boss would become the victim of a feud-related attack. He is currently in a single cell.
At yesterday's brief hearing, Detective Sergeant Sean Fallon of the garda extradition unit gave evidence of arrest, charge and caution.
He told the court that when the warrant was presented to Freddie Thompson, he said "I can't read, I'm not taking this".
He then replied "No comment".
There was no application for bail and 'Fat' Freddie was remanded in custody to appear again at the High Court next Wednesday where he is expected to apply for bail.
Thompson was supported at yesterday's court hearing by his older brother Ritchie and his long-term girlfriend Vicky Dempsey. Both looked distraught when he was remanded in custody and Ritchie spent a number of minutes talking to lawyers about the case outside the court room when the brief hearing ended.