The Netherlands international has been a key feature of Van Gaal's United side so far, with the former Barcelona and Bayern Munich boss suggesting recently the 24-year-old was a better player than his father.
Danny Blind was captain of Van Gaal's UEFA Champions League-winning Ajax side in 1995 and was his assistant alongside Patrick Kluivert at the recent World Cup in Brazil.
With Van Gaal also suggesting the midfielder had some way to go before he had the leadership qualities of his father, the close-season signing expressed his desire to become a prominent figure at Old Trafford.
Asked by the Manchester Evening News about Van Gaal's comments, he said: "I read it. I hope I become a bit of a leader like my dad was, but I am still young.
"I am still improving and this is a new era for me, coming to a new area.
"But I can be [a leader]. I have to learn it and have to keep it up but I am learning every day, including about being a leader."
Having played under Van Gaal at the World Cup in Brazil, the younger Blind is well versed in how the 63-year-old operates.
The Dutch finished third at the competition and the versatile performer now feels his United team-mates are beginning to adapt to the new regime.
"I think the players are getting used to [Van Gaal’s methods]. The players like to work with him. Everyone is picking it up very well," he added.
"Training is very hard and very serious and we improve every day and you could see that in the first half [of the 2-1 win] against Everton.
"We have seen that in the first half but now we have to see it over 90 minutes. The play is better though.
"It's important to do it [for] 90 minutes if you want to beat the big clubs. I don't think one single game is easy in the Premier League."
