The Championship promotion chasers are currently second as they bid to return to the Premier League following a six-year absence.
Karanka's team have already tested themselves against top-tier opposition this season, pushing Liverpool all the way to penalties in a League Cup third-round tie at Anfield in September.
That clash was eventually settled in Liverpool's favour after an epic 30-penalty shoot-out.
City were severely tested by Middlesbrough's Championship rivals Sheffield Wednesday in the previous round, coming from behind late to claim a 2-1 triumph.
And Karanka is adamant Middlesbrough will produce a display of spirit akin to their performance on Merseyside.
"There's a big difference between us and Manchester City, but football is football," Karanka told the club's official website.
"I know it's going to be a difficult game but we're preparing to fight face to face with them in the same way that we did against Liverpool."
Willy Caballlero is likely to be in goal for City at the Etihad Stadium, should Manuel Pellegrini continue his policy of resting Joe Hart in the Cup.
Caballero is keen to ensure Manuel Pellegrini's men keep their hopes of a place in the Wembley final intact after losing to Newcastle United in the fourth round of the League Cup.
However, the former Malaga man is not taking Middlesbrough lightly.
"Every trophy is important to us and we know that if we can beat Middlesbrough on Saturday, we will already be in the last 16 of the FA Cup," Caballero told City's official website.
"This is a trophy we have done very well in over the past three or four years, winning the cup, reaching the final and making the quarter-finals in the past four years.
"We know we made hard work of the 2-1 win over Sheffield Wednesday in the previous round and that Middlesbrough are playing very well at the moment.
"Sheffield Wednesday played very well and worked hard to make it a difficult match for us.
"We expect nothing less from Middlesbrough and with thousands travelling fans behind one goal, it makes for a great atmosphere and it also a break from the pressure of the Premier League for us."
Midfielder Samir Nasri is still out for City with a calf injury, while Frank Lampard picked up a hip problem in a midweek friendly with Hamburg.
For Middlesbrough, Ryan Fredericks (thigh), Rhys Williams (Achilles) and Muzzy Carayol and Damia Abella (both knee) remain on the sidelines.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
