The teenager has impressed since being promoted from the club's academy this season, scoring seven goals in 12 appearances, including the winner in Saturday's Premier League win over relegated Aston Villa.
“It's unbelievable, no?. This player is really young and he's scored many goals. Hopefully, for many years, he'll be in this club and can make history for the club as well,” De Gea told MUTV.
“He's a shy guy, he is a really good lad and a good team-mate. He's a really good guy.”
Louis van Gaal's men have conceded 30 goals in their 33 games so far, only Tottenham Hotspur have shipped in less, and De Gea believes their defence has played a key role in keeping United in the hunt for a place in the Champions League next season.
“I think we've defended really well this season and we need to continue until the last game and hopefully we will be in the top four. We need to win our games and wait for the rest of the teams. We will see in the end,” De Gea said.
Fifth-placed United are four points behind Arsenal, who hold the final Champions League qualifying spot, with five games left. The 13-time league champions host 16th placed Crystal Palace at Old Trafford on Wednesday.
Original source: De Gea tips Rashford to make history