Manchester United are currently sixth in the Premier League but are unbeaten in their last 16 games in all competitions.
Jose Mourinho's side are just one game away from the EFL Cup final while they face a favourable home tie in the FA cup fourth round against Wigan and are into the knockout round of the Europa League.
De Gea has won the Premier League and FA Cup during his five-and-a-half year spell at United along with three Community Shields.
David De Gea insists Manchester United are still fighting for four trophies
Manchester United are one game away from the EFL Cup final
And the Spain international has his eyes set on adding more silverware to his trophy cabinet this season.
"We are in the four competitions and we need to fight for everything," De Gea told Sky Sports.
"We are Manchester United. We are close to the (EFL Cup) final at Wembley and we need to start (preparing for that) on Saturday against Stoke.
Jose Mourinho's side are still in the FA Cup and Europa League
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"We want to keep winning. We are in a good run and we need to stay at the same level, try to win many games and then we can see where we finish in the league."
United had their nine-game winning streak come to an end last week in the 1-1 draw with Liverpool.
They return to Premier League action tomorrow when they travel to Stoke (3pm).