Herrera, 29, will be out of contract in the summer and sources have told ESPN FC that Paris Saint-Germain, Arsenal, Barcelona, Juventus and Inter Milan are interested in his signature.
And, speaking ahead of the Champions League quarterfinal first leg against Barcelona, he said he and the club are no nearer reaching an agreement.
"What I want is to beat Barcelona and think about football, Herrera told Diario ABC. "It's true that I only have two months left on my contract and as it is right now Manchester and I are not thinking alike and there is no renewal agreement.
"But my duty is still to continue to listen to United. What it's clear to me is that I will continue playing for a big team. I take care of myself for that reason, I feel well and I want to continue in football for as long as my body allows me to because the day I retire I will begin to regret to have hung up my boots.
"I will listen to United, of course, but also to other clubs. I don't close any doors."
Herrera's United teammate Pogba has been linked with a move to Real Madrid -- and boss Zinedne Zidane recently said he liked the France international a lot.
Asked about whether Pogba would fit in at the Bernabeu, Herrera added: "Pogba would be a great reinforcement for Madrid and for any team in the universe, but I hope he continues at United.
"He is a midfielder who has all the qualities. He heads well, can strike with both feet. He is quick, powerful, helps at the defensive end, he can go one-on-one, he provides assists and scores."
Meanwhile, Marcus Rashford handed manager Ole Gunnar Solskjaer a boost by taking part in training on the eve of the Champions League clash with Barcelona but Nemanja Matic, Herrera and Eric Bailly were all absent.
Rashford missed the 2-1 defeat to Wolves with an ankle injury but was able to take part in training on Tuesday morning ahead of the Champions League quarterfinal first leg at Old Trafford.
Rashford warmed up away from the main group -- working separately with a member of Solskjaer's backroom team before joining his teammates.
United booked their place in the quarterfinals with a dramatic 3-1 win over Paris Saint-Germain after losing the first leg at Old Trafford 2-0.
Barcelona beat United in the 2009 and 2011 Champions League finals.
However, they have never won at Old Trafford in four previous visits -- the last of which was a 1-0 defeat in the 2008 Champions League semifinal.
Information from ESPN FC's Manchester United correspondent Rob Dawson and Spain correspondent Adriana Garcia was used in this report.