The BBC has been told by a Muslim community worker that members of the public called the police anti-terrorism hotline about Abedi's extreme and violent views several years ago.
We don't know how the police responded to these reported hotline calls - but we have also learnt that earlier this year, Abedi's behaviour again raised concerns.
According to our sources, he told local people about the value of dying for a cause.
He also made hardline statements about suicide bombings and the conflict in Libya.
Abedi's parents fled Libya as opponents of Colonel Gaddafi's regime.
Libya, alongside its North African neighbours, has been a centre for the rise of modern Islamist political movements.
These movements were originally dedicated to overthrowing dictatorial regimes and, to varying extents, promoting the idea of Islamic government.
The Libyan Islamic Fighting Group (LIFG) wanted to overthrow Gaddafi and became the dominant revolutionary force in the country in the 1990s, until the dictator began turning the screw.
Many of those with Islamist connections tried to flee - and many of them were granted refuge in the UK.
Salman Abedi's father, Ramadan, was part of the broad network of opponents who supported those Islamist anti-Gaddafi aims. He arrived in the UK in the early 1990s.
We have been told by senior LIFG sources that he was not a member of the organisation. But he was known to be a dissident with some of the same political goals.
That brings us to south Manchester. It has long been a centre of Libyan politics in the UK, if not Europe.
It's where the British government gave refuge to many of those Gaddafi opponents - Birmingham and London being the other locations.
Some of the Libyans in the UK, and in particular from Manchester, were later suspected by the security services of being aligned to al-Qaeda.
I have spoken to some of these men down the years. They say their jihad was against Gaddafi alone. They wanted him overthrown.
And overthrow him they eventually did - with the help of the British and Americans.
As the Arab Spring grew and Gaddafi began to wobble, these dissidents - and a fair few of their British-raised sons - returned to their revolutionary roots.
Many joined the February 17th Martyr's Brigade, one of the key fighting units in that war. We have been told that Salman Abedi's father was part of the group who left the UK for one last battle against Gaddafi.
The BBC has been trying to put these questions to Ramadan Abedi. Shortly before that was to happen, Mr Abedi was arrested by security forces in Libya.