Harrison, whose one and only appearance against Ireland came when Ronan O'Gara kicked the men in green to a famous 18-9 win in November 2002, feels it is high time the Irish won the championship - particularly with the high-quality crop of players currently at Eddie O'Sullivan's disposal.
"Ireland's challenge will be to manage expectations because there is no doubt they have the ability to win the tournament," said the 32-year-old, who captained Ulster against the Ospreys last Saturday.
"Wales were faced with the same problem last year when they into the tournament as champions. Sometimes the burden of favouritism can weight heighly on a side.
"If Ireland can handle that, I can't look past them as championship winners. They have a settled side and are heading into the tournament on the back of a successful autumn."
And while Harrison's Ulster team-mate Neil Best will not be starting the championship opener against Wales, the Australian feels the tough tacking flanker can have a big impact on the Six Nations.
"Ireland have certainly acquired a harder edge in the past year and Neil has helped on that front. He is a physical player who operates right on the advantage line.
"Ireland haven't had a player like that for a while and he helps them impose themselves on opponents."