There are 61 places between the Toffees and the side currently bottom of League One, who have lost four of their last six matches.
However, Osman insists if they do not approach the fixture at Broadhall Way in the right manner they could be in for a surprise.
"That is what is so special about the FA Cup," he said.
"People look for giant-killing in each round and I think people will be hoping for one in this round with us.
"We have to go there and be as professional as we usually are, take the game seriously and show our quality on the day.
"Over a number of years we've had a couple of ties that haven't gone our way against teams we were expected to beat but we are hoping we can put a good cup run together, go to teams like Stevenage and come away victorious."
Osman was a member of the side which reached the FA Cup semi-finals in 2012, only to be knocked out by near-neighbours Liverpool having initially taken the lead.
It is a competition which remains close to the 32-year-old's heart.
"I am sure a lot of fans out there think the same as I do, that it was the showpiece occasion of the football season," he added.
"I used to watch the build-up on a cup final morning and be excited about the game.
"It shows if you can get to that cup final how important it is for players and fans and you know that starts with winning each round."
Everton's only other previous meeting with Stevenage in their 136-year history came five months ago in the second round of the Capital One Cup.
In what was manager Roberto Martinez's third competitive game in charge the Toffees came from behind to win 2-1 in extra-time.
"We have had a taste of what is to come. I am sure they will say the same," said Osman.
"I think we have probably developed as a team since that first occasion.
"We have had a lot more time to gel since then and hopefully that will show in the game."
Martinez is also not putting too much store by that result at Goodison Park in August.
"When you play away from home it is a big difference and the FA Cup brings a different approach," he told evertontv.
"When they play in front of their fans that is something we need to be able to adjust and adapt to.
"It is one of those challenges you embrace and look forward to.
"This is a phenomenal competition to be involved in and we need to be at our best.
"You need to be able to go to places like Stevenage and compete well. It has nothing to do with how well we have been playing so far."
Everton are still awaiting news on the completion of their loan deal for Monaco forward Lacina Traore.
Earlier in the week the move seemed a formality once the Ivory Coast international had obtained a work permit but since that paperwork was secured there has been the added complication of a knee injury to the French club's leading striker Radamel Falcao.