Middlesbrough were the pre-season favourites to win the Championship, but Garry Monk's team currently sit in 13th position in the table after winning just four times in 13 matches.
However, Howe has said that he is anticipating a hard tie as both clubs look to secure a rare place in the last eight of the competition.
The 39-year-old told reporters: "We had some tough games against Middlesbrough last year. They beat us at their place, they beat us here. I have full respect for Garry Monk and his Middlesbrough squad.
"Nothing is easy in this game and it will be a really tough game. The quarter-finals await the winners. We won't view how we prepare for the game any differently, but the games take on a different meaning I think. This is the most important one - the next one."