The Cherries, 40 places below Roberto Martinez's men, beat Dagenham and Carlisle to set up the tie at the DW Stadium, and Fletcher says stranger things have happened than Eddie Howe's men, unbeaten in 11 games since he returned for a second spell, making it to the fourth round.
"There have been bigger shocks in the FA Cup and we won't be going there to make up the numbers," the 40-year-old, who stepped off the bench late on at Brunton Park, told the Bournemouth Daily Echo.
"They are a very good side, but even though they are an established Premier League club, we have to go there believing we can get a positive result.
"We believe we can go there and possibly cause an upset. We have to believe that
"A lot of factors would have to go our way and if Roberto Martinez plays his strongest side, we will be right up against it.
"But he could make one or two changes and, if we are at our best from one to 11, we could come away with a good result."
The cup-tie, Fletcher's first match at the home of the Latics for 11 years, will take place on the weekend of January 5/6 2013.