London's Sunday Telegraph newspaper has reported that Blair in a personal capacity wrote to Janice Kelly after the publication of the Hutton inquiry report offering to meet her, but the dead expert's widow is yet to respond.
The newspaper quoted a Kelly family-friend as saying that the widow remained "very angry" with the government.
Kelly killed himself last July after being identified as the source of a controversial BBC report alleging Blair's government had sexed up the threat from Iraq's weapons of mass destruction to justify the war.
Janice Kelly, who has already met Defence Secretary Geoff Hoon, told the Hutton inquiry that her husband felt "totally let down and betrayed" by the way his identity became public.
The unnamed family friend told the newspaper that she was "more angry" with the Ministry of Defence than with the BBC.
"I don’t think she would want to meet Geoff Hoon but she may find the offer of a meeting the Prime Minister irresistible," the friend added.
A spokesman for Blair offered no comments on the matter.