Coyle, who took Burnley to the FA Cup fifth round and Carling Cup semi-finals last season, has already seen Bolton give combative performances home and away against Arsenal since being appointed as manager a fortnight ago, and the Scot thinks his new side have as good a chance as anybody of making it to Wembley.
"I think it's a good year for any club to be thinking it may be your time," Coyle said.
"You always must have that feeling that you can go and achieve in football and that's what I'll be driving home to my lads.
"So yes, why not? We've shown in the last two games that we can stand toe-to-toe with the best.
"We have to make sure we earn the right to do that by progressing in the cup against difficult opponents, opponents I know well from our tussles last year.
"We'll be very respectful of the qualities they have, but equally I want my lads to be expressive and show their qualities at the Reebok Stadium, and go and give another performance."
Tomorrow's encounter will pit Coyle against Sheffield United for the first time since Burnley's victory over the Blades in last season's Championship play-off final.
Burnley triumphed that day, but Coyle has been impressed with the resilience United manager Kevin Blackwell has shown since then to move on from the crushing disappointment and mount another promotion challenge this season. They are currently sixth in the Championship.
"I know how tight the margins are and I think I showed that in my interview after the game, because it could easily have been us on the other side of that," Coyle said.
"Kevin is a terrific manager and he has done a fantastic job, and I think that has been borne out now when you look at where Sheffield United are.
"There was always going to be a period in the season where there would be some sort of fall-out from losing out in the final, because it's such a huge game in terms of winning it or not and what it means to a football club.
"But they have come through that and Kevin has shown unbelievable qualities as a manager to mould that group and bring a little bit of freshness in.
"Now they are back in the play-off positions and getting stronger by the week, so we have to make sure we are at our best because it's a tough tie."
Coyle will be without Mark Davies for tomorrow's match after William Gallas' tackle on Wednesday left the midfielder with ankle ligament damage.
Davies had to be taken off on a stretcher after the controversial challenge during Bolton's 4-2 defeat at the Emirates Stadium and it is not yet known how long he will be sidelined for.
The tackle, just prior to Arsenal's equaliser in a game Bolton had led 2-0, went unpunished by referee Alan Wiley and Gallas is unlikely to face retrospective disciplinary action from the Football Association.
Coyle likened the challenge to an "assault" in a post-match interview but today indicated he did not think Gallas intended to hurt Davies.
"Maybe (to say) an assault was a bit strong," Coyle said.
"But he certainly caught the lad. I don't think that any professional, and I would certainly hope not, goes to purposely hurt another player, but it was mis-timed - there is no doubt that it was badly mis-timed.
"Mark Davies paid the price for that and we did as a team because with a player lying on the ground, they have scored an equaliser."