The paper noted that it was aware of the identity of the family member and full details of the role played, but had agreed to protect anonymity.
According to the report, veteran Israeli peace activist Gershon Baskin was at the center of attempts to open negotiations. He was in touch with senior members of Hamas, Israeli officials and Olmert, via the member of his family.
For over two years after the abduction of Israel Defense Forces soldier Gilad Shalit, Hamas officials expressed a willingness to talk to Israel directly about the kidnap, conditions for a new ceasefire and the ending of the blockade, the report said.
According to The Observer, the motivation - from Hamas' side - stemmed from a growing frustration with the role of Egypt as an intermediary over key issues between the two sides, especially in relation to ceasefires.
'Hamas offered direct talks'
Baskin told The Observer he believes the failure to pursue the overtures was a lost opportunity that contributed to the outbreak of conflict.
"Three times since Shalit's kidnapping (in June 2006) there has been the suggestion of opening a back channel through me." He said. "The first time that Hamas suggested to me opening a secret back channel was not long after Shalit's kidnapping."
According to Baskin, that offer was immediately rejected by the office of Olmert, who said Israel did not negotiate with terrorists.
His contacts, said Baskin, were two-fold. On the Hamas side, his contact was a senior figure whom he met in Europe, who was close to the organization's leaderships both in the Syrian capital Damascus and the local leadership in Gaza.
His liaison with the Hamas official focused on two issues: Opening secret and direct contacts, and linking the prisoner exchange for Shalit's release to the renewal of the ceasefire and the ending of the economic siege on Gaza.
Baskin's "messenger" to Olmert on the Israeli side was the family member. "I was getting messages to Olmert through (this person)," he said. "And what I was getting back from Olmert through the same route was: 'We don't negotiate with terrorists'."
As part of this communication, the report said, Hamas offered a video proving Shalit was still alive, which would be supplied in exchange for the release of some women and other minor prisoners from Israeli jails.
Olmert's response, said Baskin, was that they did not need the video as Israel had already established that the soldier was alive. While that was rejected, the contact did, however, lead to a letter from Shalit to his father, Noam.
A year after the first contacts, Baskin told The Observer, he had been given approval to pursue an informal effort to open secret direct contacts, coordinating with Ofer Dekel, the official appointed by Olmert as his "special representative" to head efforts for Shalit's return.
This time, however, it was Hamas' turn to block the opening of the secret negotiations - rejecting the linking of the prisoner exchange with the ceasefire and the end of the siege.
Baskin said he had persisted with his dealings with Hamas, communicating with his contact through scores of emails, some passed on to the leadership in Syria and Gaza.
Two years after his first contacts through the Olmert family - and with war looming - Baskin said he tried to use his contact again. "I only involved (the person) one more time. I was desperate to get a message to Olmert."
With the conflict only two weeks away Baskin arranged a meeting with his key Hamas contact in Europe, which resulted in another offer to link Shalit to the lifting of the ceasefire. However, nobody on the Israeli side replied to the final offer.