Pogba will remain captain for the Brighton game, although Mourinho explained that Antonio Valencia will reclaim the armband when he returns to action following a calf injury.
Herrera joined Manchester United from Athletic Bilbao in 2014 and his current contract is set to expire in the summer of 2019.
Barcelona have signed Brazilian duo Malcom and Arthur this summer.
Pogba cost United a then-world record 89 million pounds (105 million euros, 116 million dollars) in 2016.
Paul Pogba had been linked with a move away from Old Trafford with Barcelona's interest reportedly piqued by his frosty relationship with Jose Mourinho.
Fresh from inspiring France to win the World Cup, Paul Pogba is hungry to win more trophies for Manchester United after captaining the Red Devils to a winning Premier League start with a 2-1 victory over Leicester on Friday.
Luke Shaw sealed the points seven minutes from time before Jamie Vardy headed home a consolation for the visitors.
Following a successful summer in which he helped France to win the World Cup, Pogba's future at United has been the subject of speculation over the last week of the Premier League transfer window.
Liverpool weren't just the biggest spenders, but got their business done early and improved the key areas of Jurgen Klopp's squad that needed strengthening.
Yerry Mina scored three times in three games in Russia.
Manchester United have to defy their own manager Jose Mourinho's fears for a season of doom and gloom when they kick off the Premier League campaign against Leicester City on Friday.
The reported agreement would see him pick up 346,000 euros a week, almost double what he earns at United.
Manager Jose Mourinho has already predicted a "difficult season" if United do not do more business before the Premier League transfer window shuts.
Jose Mourinho admitted that he may not have his ideal side at his disposal when Manchester United open their Premier League campaign on Friday.
Javi Martinez nodded in from a corner on 59 minutes as the German champions overcame a lacklustre display from Jose Mourinho's side.
Paul Pogba was part of the FIFA World Cup winning French team.
Jose Mourinho was finally given something to smile about as a tempestuous trip to the United States ended with a 2-1 victory over former club Real Madrid thanks to first-half strikes from Alexis Sanchez and Ander Herrera.
Jose Mourinho hit out at Manchester United's transfer window inactivity after watching his squad crash to a 4-1 defeat against Liverpool.