Investigators managed to extract new information from a laptop discarded in a rubbish bin by Ibrahim El-Bakraoui, one of the airport bombers, in which they had already found his audio "will", according to the reports.
The computer files show the bomber discussed attacks in "other European countries" besides Belgium, starting with France.
"Great Britain is also mentioned as a potential target," a Continental intelligence source said.
A Whitehall source said the discussions involving British targets were aspirational rather than specific plots.
Under a file named "Target" in English found on the laptop, the bomber then refers to striking La Défense the Paris business district, and the ultra-conservative Catholic organisation, Civitas.
BFM TV, the French rolling news channel also said investigators obtained a taped conversation between Najim Laachraoui, the suspected bomb maker for the Paris and Brussels attacks, and a "foreign contact" in which Britain is also mentioned.
The contact was not understood to be based in Britain but may have been a "mastermind" working out of Syria.
However, the pair decided the UK was "too complicated to strike, that Belgium should remain their operational base and so they should hit France".
Arrested last weekend, Abrini, a 31-year-old Belgian of Moroccan origin, has confessed to being "the man in the hat" seen on CCTV at Brussels airport shortly before two suicide bomb blasts went off on March 22.
He left a bag packed with explosives before calmly walking away. The attack and a later explosion at a metro station killed 32.
Abrini's visit to Britain was recently confirmed by Interpol president Mireille Ballestrazzi on the BBC's Panorama, which said photos of an unspecified British football stadium were found on Abrini's phone.
