The Cherries lie eighth in the table ahead of Tuesday night's clash with Leyton Orient at Dean Court, following a run of just one defeat in nine matches. And veteran striker Fletcher thinks that, after a disappointing start to the campaign, the Dorset club have the quality to make the top six.
"We've given ourselves a chance of doing the impossible and getting into the play-offs. It's only a chance but we could be in among it," he told Press Association Sport.
"We jumped 10 places in about four games with a run of form to get where we are now but we know it's going to be tougher to get into the top six.
"You can ride on the crest of a wave for a while, but then you look at the teams at the top and some people are saying it's already decided. With Charlton, Sheffield United, Sheffield Wednesday, MK Dons - there's probably only one place there up for grabs.
"Then there's us, Notts County, Carlisle are up there, Stevenage - lots of teams all looking to get there. We know it's a tough ask but it's something we have to be looking to do."