Nancy Soderberg said the Northern Ireland peace process was a large part of Mr Clinton's legacy as US president.
"This is something he cares very deeply about, and if there's a way he can help, of course he would be willing to," she told the BBC's Sunday News.
Northern Ireland's political parties have been holding round-table talks.
It follows a row sparked by a police assessment that IRA members were involved in murdering a former IRA man.
In the wake of the killing of Kevin McGuigan Sr, police said the IRA still existed, but added that it was not engaged in terrorism.
Three Democratic Unionist Party (DUP) ministers subsequently resigned from Northern Ireland's ruling executive, and Peter Robinson, the party's leader, stepped aside as first minister.
Mr Clinton's offer of assistance was made public on Saturday by Irish prime minister Enda Kenny, who met him last week in New York.
Ms Soderberg said the ultimate responsibility for achieving progress lay with the Northern Ireland parties.
In an Irish Times article last year, she accused Northern Ireland politicians of an "abysmal abdication of leadership" and being "stuck in the past".
Asked if this was still her view, she said: "The fact that you need to call back Bill Clinton to move things forward is evidence that this remains true.
"That's not to say that this is easy - I don't mean to sit over here on this side of the pond and just throw darts, but after all that Washington has invested in this, as well as London and Dublin, the fact that they're still questioning whether you can have a devolved government is quite stunning."
She added: "It should give the leaders pause to say 'what's missing in this equation?'
"My view is it's trust - this generation doesn't trust itself and what it's not doing is cultivating the next generation that will."
Northern Ireland Secretary Theresa Villiers said on Thursday that this week's talks had been "useful and intensive".
Ms Villiers said the talks would resume on Monday to "discuss the impact of continued paramilitary activity".
Bill Clinton has a genuine willingness to help Northern Ireland parties resolve the crisis at Stormont, a former senior aide has said.