The Spaniard led Wigan Athletic to the crown last term, their first major trophy, as Ben Watson's injury-time winner secured a shock 1-0 triumph over Manchester City in May.
Wigan were subsequently relegated from the Premier League and Martinez departed to take the vacant post at Everton.
The Merseyside outfit have good pedigree in the FA Cup, collecting the famous trophy on five occasions, most recently in 1995 when Paul Rideout sealed a 1-0 victory over Manchester United.
Everton have also finished runners-up on eight occasions, more than any other side, with their last final appearance coming in a losing 2-1 effort against Chelsea in 2009, while their tally of 13 final appearances is bested only by Manchester United, Arsenal and Liverpool.
Having endured a hectic end-of-year period, Martinez may decide to rotate his squad, and back-up goalkeeper Joel Robles is hoping for a chance to shine.
Speaking to the club's official website, he said: "I'm working hard to make myself available for both cup and league games. If he (Martinez) wants to put me in, that would be great."
QPR, relegated from the top flight alongside Martinez's Wigan last term, are sure to prove stern opposition having enjoyed a solid first half to the campaign, as Redknapp attempts to secure an immediate return to the top flight.
The Loftus Road outfit are third after taking 46 points from 24 matches and are just one point adrift of the automatic positions in the Championship.
Striker Charlie Austin has been a key component of their success, with the former Burnley man notching 11 league goals thus far, including an injury-time winner in the 2-1 triumph over Doncaster Rovers on New Year's Day.
Austin had missed the previous two fixtures, as QPR drew blanks against at Nottingham Forest and Watford, but the forward says the burden is on everyone in the team to perform, not just him.
"I understand it when people talk about pressure being on my shoulders, but scoring goals is my job," he told club's official website. "There's no more pressure on me than there is on anybody else."
