Pogba was a target of online abuse after he missed a penalty in Monday's 1-1 Premier League draw at Wolves.
Chelsea boss Frank Lampard last week urged social media companies to take action after 21-year-old striker Tammy Abraham was targeted after the team's UEFA Super Cup loss to Liverpool.
"We have always maintained an open and healthy dialogue with our partners in this space, but we know we need to do more to protect our users," Twitter said in a statement.
"Racist behaviour has no place on our platform and we strongly condemn it.
"Over the next few weeks, Twitter representatives will meet with Manchester United, Kick It Out and any other civil society stakeholders interested in hearing about the proactive work Twitter is doing to address online racist abuse towards certain footballers in the UK."
The abuse suffered by Pogba was condemned by his team mates including Harry Maguire who urged social media companies to verify user accounts to prevent anonymous abuse of players.
England women's coach Phil Neville, a former United player, urged the soccer community to boycott social media for six months to send a message.
A study released by Kick It Out said it received 159 reports of discrimination via social media in the English professional game last season.