Shaaker is set to take legal action against the British Government after being released from the US prison camp, sources say.
The father-of-four is spending his first full day of freedom in Britain after being detained for 13 years without charge at the camp in Cuba.
He is being treated in hospital and is due to meet his children this weekend after being reunited with wife Zin.
Mr Aamer’s youngest son Faris was born on the same day Mr Aamer arrived at Guantanamo Bay in February 2002.
He flew in to Biggin Hill airport in south-east London by private jet on Friday afternoon. He thanked campaigners who had called for his release, saying: “Without their devotion to justice I would not be here in Britain now.”
The 46-year-old is understood to be planning to bring legal proceedings against Britain for its alleged complicity in his mistreatment at the hands of the US military.
A source said: “Proceedings were initiated some years ago on his behalf that could not be followed until his return to the UK. They will now, undoubtedly, be progressed.”
The source added that reports of Mr Aamer being in line for a compensation payout in the region of £1 million were “speculation”.
Lawyer Clive Stafford-Smith from the human rights campaign group Reprieve told the BBC: “We had a promise from the Prime Minister that there would be a fully independent inquiry into all of this torture. Unfortunately that’s not happened yet.
“This is a huge priority of Shaker’s. He doesn’t want to have people persecuted. He doesn’t want to have small people, who were sent out to do their jobs, prosecuted for what they did.
“What he does want is that the whole world should know what did happen so we can set in place rules so that British agents and, let’s hope, American agents don’t get involved in the torture business in the future.”
One of Mr Aamer’s lawyers, Ramzi Kassem, said he was suffering from various medical conditions including post-traumatic stress disorder.
Mr Aamer’s lawyers claim he was tortured in Guantanamo and held in solitary confinement for 360 days. In 2005, he lost half his body weight during a hunger strike.
After returning to the UK, Mr Aamer paid an emotional tribute to those who fought for his release, saying: “Without their devotion to justice I would not be here in Britain now.”
The 46-year-old arrived on a private plane at Biggin Hill airport in south-east London yesterday afternoon.
Mr Aamer has said he was seized by bounty hunters while working for a charity in Afghanistan in 2001 shortly after the September 11 attacks.
The Saudi national was handed over to US forces and was transferred to Guantanamo in February 2002 after being accused of helping al-Qaeda.
In 2007 the allegations against him were dropped and he was cleared for release. But the US authorities refused to let him go home despite a formal request from the then foreign secretary David Miliband.