The 21-year-old midfielder continues to impress after returning to the Gunners side in late October last year following 15 months out with an ankle injury.
The England international scored the only goal as part of a man-of-the-match performance as Arsene Wenger's side beat Swansea 1-0 in an FA Cup third replay on Wednesday.
Wilshere said: "Do I feel like a leader? That is part and parcel of my game and is the type of player I am - I like to pick the ball up, run at players and drive the team on. We all need to show a bit of character now.
"We knew we needed to get a result against Swansea and we all applied ourselves excellently in that game.
"We want this cup - it is a big competition. It was the last major trophy we won and we know what it means to the fans to get a trophy."
This Sunday, Arsenal face third-placed Chelsea, who are eight points and three places above the Gunners in the Premier League table, but Wilshere is confident his side can beat the Blues at Stamford Bridge , as they did last season.
"Chelsea don't like playing against us. We play football so if we can take the game to them and get in behind them, we can cause problems," he said.
"We won there 5-3 last season, so we know we can do it and we have to be
confident going there. We have to take the game to them and play our football because we are a bit behind in the table and we need points."