The Lady Black Cats are one of only two teams from outside the Super League to reach this stage and the Premier League leaders are looking to pull off a memorable victory to move into the semi-finals.
And Gutteridge is hoping she can score for the fourth successive game to help seal progress.
I had a spell without scoring this season and it was a relief when I finally did manage to score, she said. Ive now got three goals in the last three games, so hopefully I can contribute with a few more.
I have moved to a new position this season, playing as the advanced player in a midfield three. It allows me to get forward as much as possible and link up the play, but I also need to get back to defend when the opposition have the ball.
It isnt much different from the position Ive played in the past. Ive always played as a second forward who drops deep to receive the ball.
I didnt really let the lack of goals bother me too much, as we have been winning games and we score plenty of goals as a team.
While Sunderland are favourites to retain their Premier League title, they know a trip to Birmingham who were just beaten to the inaugural Super League title by Arsenal last season will be a major test.
Birmingham are a team full of quality international players, so it will be tough for us, said Gutteridge. But its a game we are all really looking forward to. Its an exciting challenge for us and will give a good indication of our progress against one of the best teams in the country and one of the favourites for this competition.
Weve been performing well recently so well go into the game full of confidence and give it everything weve got. Were the underdogs and have nothing to lose. As a Super League team, the pressure is on Birmingham.
The league is in our hands with two games remaining and were hoping for a good run in both cup competitions, so its an exciting end to the season for us.
Arsenal play Everton in another quarter-final, which sees Wearsiders and England team-mates Steph Houghton (Arsenal) and Jill Scott (Everton) on opposing sides.
Bristol Academy face Blackburn Rovers, while Doncaster Rovers Belles take on Chelsea on the other games.
Courtesy of Neil Watson, Sports Editor, Sunderland Echo