Chief executives' body Acevo sent an email to the groups involved this week, warning that Mactaggart has been "expressing frustration that the sector is bickering, and has said if we can't come up with an agreed approach she is tempted to hand it over to the private sector".
Acevo chief executive Stephen Bubb sought to play down the warning when asked about it by Third Sector. He said he had not spoken personally to the minister, but had heard that she was annoyed to learn of the tensions between the rival IT alliances Citra and the ICT Consortium.
However, he was quick to insist that Mactaggart had no need to carry out her threat "because we are getting it sorted out".
He said: "We had a very productive meeting last week. We are going to appoint an independent chair chosen by the two sides, and I am optimistic it will get sorted."
Nick Aldridge, Acevo's head of policy and communications, added that the voluntary sector was being asked to do something it had never done before and it should not be surprising if there were "hiccups" along the way.
"The hub is bringing together all these sides that are used to competing on various things, so some minor skirmishing is inevitable."
He said Acevo's warning of private sector intervention "was not based on very much", but gleaned from "various conversations with certain people in Government".
"It was not a particular person with any seniority saying this is a real option ... it is just one of a number of ways that could deliver what the hub is going to do," he explained.
However, Aldridge echoed Bubb's assurance that the sector was well on the way to presenting a united front.
"Last week's meeting was positive and we have a process now. The tone has changed, and people are being much more positive," he said.
Mactaggart's office refused to be drawn on the issue, saying that it never commented on speculation.