Everton take on Norwich City tomorrow in the Capital One Cup.
Everton have managed to get past Barnsley and Reading in the competition so far this season, and they face Norwich City in the next round on Tuesday.
The Toffees still have four rounds left to get through if they are to life the trophy in February, but Deulofeu believes that they have a chance of going all the way.
"Why not?” he responded, when asked if Everton can win the League Cup this season. “The Capital One Cup and FA Cup are good challenges and Everton need to [try and win] these cups.
“It’s a good game against Norwich. Playing at Goodison, we need to win for the confidence of the team.
“If we win, we go to the quarter-final. It’s a challenge and I want to win the game.”
The likes of Arsenal, Chelsea, Liverpool, Manchester City and Manchester United are all still left in the competition, meaning that Everton's task of winning the tournament looks a tough one.
However, Roberto Martinez's side definitely have a chance, if they can overcome Norwich tomorrow evening.
Everton go into that game having lost their last two Premier League fixtures, and they will be eager to bounce back against a Canaries side, who have proven to be a threat this season.
Norwich have picked up some impressive results since being promoted back to the top-tier, but they have failed to win any of their last four matches.