Wayne Rooney is likely to give up the armband this summer amid talk that he is set to move away from Old Trafford.
Rooney has held the honour of being club captain since 2014 when he took over from Nemanja Vidic.
Sections of the United support have called for Herrera to be named captain if Rooney leaves the club because of his belligerent attitude on the pitch.
But the 27-year-old insists that he has not earned the title of captain yet.
“I am very thankful for the people who think so… but I prefer to be careful with that,” Herrera told Sport360.
“All the United captains have won everything for the club but I haven’t done yet.
“Hopefully one day I can. But to be honest I just want to keep playing and improving.”
Herrera was named United’s player of the season after his no-nonsense attitude took him from being a bit-part player under Louis van Gaal to being one of Jose Mourinho’s prized assets.
The Spaniard insists that he just wants to be known as a players who have given his all – regardless of his performance level.
“I have been really happy at United since the first day,” he said. “The only thing I can do is to give everything every game and every minute of the time I am on the pitch.
“I think the fans have the same view: I can play sometimes good, sometimes not as good but the only thing I try to do is give everything.
“That’s what our fans want. They can forgive you if you miss a pass or make a mistake but as long as you give everything, that is what they want to watch.”