The former leader of Scottish Labour has been told by police that his and his children's details were found in the paperwork of the former NoW private detective Glenn Mulcaire, dating back to when McConnell took office as first minister in 2001.
McConnell, who led the Scottish executive until 2007, has started legal proceedings against News International and has been joined in the action by his daughter Hannah, 33, and son Mark, 28.
In what is the most significant hacking allegation so far in Scotland, it is understood that the Metropolitan police are investigating other potential data breaches against McConnell, in addition to the alleged hacking of the family's mobiles.
"The initial intrusion appears to start early in Jack's time as first minister but the family and the police don't seem to be ruling out anything at this stage," a source close to the family told the Guardian.
A family friend told the Sunday Mail: "Jack is angry that this might have happened to him but is absolutely furious that someone could have been interfering in the private lives of Hannah and Mark."
The Scottish Labour party has ratcheted up the pressure on Alex Salmond, McConnell's successor as first minister, over his close relationship with Rupert Murdoch and his son James. It emerged at the Leveson inquiry last week that Salmond offered to lobby the UK government on behalf of the Murdochs to support their proposed takeover of BSkyB, just as he was seeking the support of the Scottish edition of the Sun in last year's Holyrood elections.
Margaret Curran, the shadow Scottish secretary, said Salmond and the Scottish National party should put the integrity of the Scottish parliament before their dealings with the Murdochs.
"The Scottish government's response to this growing scandal is weak and insufficient. Their story changes by the day and is utterly self-contradictory. They are treating people like fools in order to cover up their own murky deals with the Murdochs," Curran said.
"Our Scottish parliament was meant to do things differently, meant to set higher standards. On this issue, that has not happened and Scotland is the poorer for it. This is a test of the Scottish parliament and a test of the SNP's commitment to it."
Salmond has said he offered to support the BSkyB bid in the interests of protecting Scottish jobs, and argued that other news organisations have been implicated in hacking and illegally accessing confidential data.
He has brushed off complaints that he was the only party leader to deepen his personal dealings with Murdoch after it emerged in July last year that the NoW had hacked Milly Dowler's phone.
In February, Salmond hosted a lunch at his official residence, Bute House, for Rupert Murdoch, Tom Mockridge, the News International chief executive, and Frédéric Michel, the News Corp lobbyist who facilitated contact between Salmond and James Murdoch.
The previous weekend, the launch edition of the Sun on Sunday had revealed Salmond's preferred date for the Scottish independence referendum, and Murdoch had sent out admiring tweets about Salmond.
Salmond told BBC Radio 4's Today programme on Saturday: "I think Rupert Murdoch is one of the most substantial figures in journalism for the last 50 years, so it would strike me as important to have a good and businesslike relationship with him.
"The idea that malpractice and potential illegality is confined to one newspaper organisation is for the birds."
On Sunday, a spokesman for Salmond said the first minister had welcomed the closure of the NoW over the hacking allegations, but would not comment directly on Scottish Labour's complaints about Salmond's links to the Murdochs.
He added: "It is disgraceful that Mr McConnell and his family could have been subjected to such intrusion. The first minister condemns outright all examples of phone hacking and other press malpractice, regardless of who the victims are and who the perpetrators were. In addition, he has every confidence that Strathclyde police will vigorously pursue, without fear or favour, any evidence of criminality committed against any Scottish citizen."
Until now, the most significant Scottish hacking cases centred on the disgraced Scottish socialist leader Tommy Sheridan and other figures involved in a NoW investigation into his extramarital affairs and visits to a swingers club.
It is suspected that phones belonging to McConnell's children may have been targeted because his own answering service was pre-set to send callers to a paging service. There is no evidence, however, that his wife, Bridget, a prominent council executive in Glasgow, was also targeted.
McConnell was suspicious during his time as first minister about the source of newspaper stories about his private life. He was first told of the hacking suspicions several weeks ago by Strathclyde police on behalf of the Met.
