Stuart Gray's men face fellow Championship outfit Charlton in the last 16 at Hillsborough on Saturday aiming to reach the quarter-finals for the first time since 1997.
That would then put them only 90 minutes away from Wembley, where the Owls have not been since their four visits to the national stadium under Francis in 1992/1993.
The Owls were beaten in the League Cup final by Arsenal and, after beating city neighbours Sheffield United in the FA Cup semi-final, they again met the Gunners and were only defeated by a 120th-minute goal by Andy Linighan in a final replay.
And Francis reckons that if the Owls can negotiate past Charlton, they can dare to dream of Wembley.
"It's a great opportunity because many of the top clubs are playing each other so some of them will go out," said Francis. "It is a favourable draw.
"Wednesday aren't having a great season, but they are playing a club in the same division who are below them.
"They have home advantage so they will see it as a great opportunity to get through to the quarter-finals and it could help with confidence if they were to get a win.
"I am sure they will be thinking back to 1993 and, as a former manager, when you are in the FA Cup you don't really see Wembley as a possibility until you get through this round.
"Once you get into the quarter-finals you will be thinking that this is your year."
Francis, who managed at Hillsborough between 1991-1995, admits to still having regrets over that final defeat to the Gunners, where his side were seconds away from a penalty shoot-out until goalkeeper Chris Woods inexplicably let Linighan's header slip through his hands.
"I don't have nightmares about it, but I often look back and think, 'what may have been'," he added.
"When that header came in I would have expected Chris Woods to save it. If he had saved it we'd have taken the game to penalties.
"I just keep thinking over the years I would have liked to have had that opportunity to do that so it's a case of what might have been really."
Many people in the South Yorkshire region are hoping that both the Owls and local rivals United, who play Nottingham Forest on Sunday, can progress through to the last eight, where they could be drawn against each other.
It would be their first meeting in the FA Cup since that semi-final 21 years ago and although Francis acknowledges what an occasion that was, he is not too keen on another this year.
"Back in 1993 we played Arsenal on three occasions, but for many Wednesday fans the highlight was the semi-final against Sheffield United," Francis said.
"It was a marvellous occasion, 90,000 from Sheffield at Wembley, so there is a possibility of a Sheffield derby.
"I hope Wednesday get through, but don't want United to get past Forest."
FA Cup Legend Trevor Francis was talking at the launch of the Beko Keepy-Uppy Challenge at Sheffield Wednesday. Beko will donate £1 for each entry to Barnardos www.beko.co.uk/keepyuppy