Mr McGuinness told Wednesday's Daily Telegraph newspaper he believed his party was only four points behind the Ulster Unionists and would see gains in the coming elections.
"More young people, more new voters are supporting Sinn Fein than any other party," he says.
"There's almost an inevitability that within the next five years Sinn Fein then will be the largest party and the first minister will be a Sinn Fein minister.
"I could certainly see Gerry Adams as first minister."
" I could certainly see Gerry Adams as first minister "
Mr McGuinness confides in the interview his political heroes include the labour politician Tony Benn and he has more words of praise for another British politician: Tony Blair.
Referring to the decades of the Troubles he says: "I regret the fact that through all those years we didn't have a man like Tony Blair in the British Government who was prepared to tackle the tough questions.
"Everybody is collectively responsible for what happened, but I firmly believe that those chiefly responsible were the political leaders.
"Nobody has clean hands."
Mr McGuinness refers to his decision to give evidence at the Bloody Sunday tribunal and his admission that he was the IRA's second-in-command in Londonderry at the time.
He admits to wondering about the public reaction before he made his statement but says: "With the exception of the DUP the vast majority of people have been absolutely tremendous."
Mr McGuinness, who is contesting the Mid-Ulster seat he won from the DUP in 1997, concedes that he enjoys his other political role as education minister.
"I like doing the job because I have the power to change things.
"It's part of the unique political agreement that we all reached."
The other candidates contesting the Mid-Ulster seat are Francis Donnelly(Workers Party), Eilis Haughey (SDLP) and Ian McCrea (DUP).
Meanwhile, speaking on the BBC's Newsline programme on Wednesday evening, Gerry Adams said that while his party was still seeking to use offices in Westminster, the Sinn Fein MPs would still not take up their seats because they refuse to take the oath of allegiance to the Queen.
However, he said that he felt that the politcal focus was moving away from Westminster, with low Commons attendance by the Northern Ireland parties, and that the island of Ireland was becoming "more and more the centre of gravity".
He added: "My ambition, if I have any ambition, it is to be the representative for west Belfast in an all-Ireland parliament."