The Teesside outfit tackle Tottenham on Wednesday evening in the quarter finals of the competition, seeking to inch a step nearer towards the final.
Boro have twice been runners-up in the tournament in the past decade and young defender Davies is dreaming of a final spot.
Davies is optimistic Boro can reach the competition's showpiece and is hoping he will be involved if the team progress that far.
"We are playing well now and we have been doing really well in this competition," said Davies.
"If you look at it, we are two games from the final and it would be a massive achievement for the club if we can win it and, hopefully, I can be a part of that.
"The buzz has been going round the club. Everyone is talking about it and excited about it."
Jonathan Greening is confident Boro can claim a victory at White Hart Lane given their good recent record in North London.
"Over the last few years, we have had some good results down there," said the midfielder. "Last year we beat them 3-0.
"Hopefully we can go there, play some good football and if we get an early goal, it might give us some confidence to push on."
