The Spaniard guided Wigan Athletic to a surprise win over Manchester City in last season's final at Wembley before leaving to succeed David Moyes at Goodison Park
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 Goodison Park.
Everton have good pedigree in the FA Cup, collecting the trophy on five occasions, most recently in 1995 when Paul Rideout sealed a 1-0 victory over Manchester United.
|14/1||Everton are 14/1 with Paddy Power to beat QPR 4-0|
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 Harry Redknapp attempts to secure an immediate return to the top flight.
The Loftus Road outfit are third in the Championship after taking 46 points from 24 matches and are just one point adrift of the automatic promotion positions.
Striker Charlie Austin has been a key component of their success, with the former Burnley man notching 11 league goals this term, 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."