Karenzi Karake, 54, the head of Rwanda's intelligence services, was due to meet Alex Younger on 18 June.
But the meeting was cancelled at the last moment, according to sources. The general was arrested two days later.
Gen Karake has been granted Â£1m bail by Westminster magistrates ahead of a full extradition hearing in October.
Gen Karake appeared in court on Thursday wearing a green and yellow jumpsuit. He has been held since Saturday at Belmarsh high security prison in east London.
Lawyers acting for him, including Cherie Booth QC, made it clear they believe the charges against him are politically motivated.
He was arrested at Heathrow airport on Saturday under a European Arrest Warrant on behalf of authorities in Spain.
Gen Karake is accused by Spain of ordering massacres in Rwanda in the wake of the 1994 genocide there.
Whitehall sources neither confirmed nor denied details of MI6's engagement with Gen Karake.
Nick Hopkins, BBC Newsnight's investigations correspondent, said the claim that Gen Karake had been due to meet Britain's most senior intelligence official was embarrassing for the British government.
He said the Rwandans "feel such a sense of betrayal over all this".
"One of the things that became clear at the [court] hearing is that Karake's lawyers will be relying on the fact that he should have had diplomatic immunity - he was here on official business," our correspondent said.
"So I am sure that they will be seeking from the Foreign Office some kind of confirmation that he was here to see his counterpart."
The Rwandan spy chief arrested in the UK over alleged war crimes had travelled to London to meet the head of MI6, sources have told BBC Newsnight.