Michael Laudrup's side have already made it through to the semi-finals of the Capital One Cup, with Chelsea standing between them a memorable day out at Wembley.
They will be back in cup competition this weekend when they play host to Arsenal in the third round of the FA Cup and, having already beaten the Gunners 2-0 in the Premier League this season, Michu claims Swansea are determined to edge a step closer to major silverware.
The Spaniard, who bagged a brace at the Emirates in December, said: "That win at the Emirates was good, and to score two goals as well. But I always want more. We are taking the cups very seriously.
"We're in the semi-finals against Chelsea in the Capital One Cup and now we have a difficult game against Arsenal. But the FA Cup is a big competition and we want to do well in it. We're trying to win both.
"It is going to be very difficult in both games but we are going to try.
"Sometimes it is the small clubs against the big clubs, but the draw has not been kind to us. But we have had good results against Arsenal and Chelsea this season, so why not?"