The Argentina winger arrived in Manchester United F.C. on Monday and would have a medical test later on today, British newspapers said.
The transfer fee outstrips the 50 million pounds English Premier League rivals Chelsea paid Liverpool for Spain striker Fernando Torres in 2011.
Manchester United declined to comment.
Angel Di Maria cost Real Madrid 20 million pounds from Benfica in 2010 and he was a key part of the team that won the club's 10th European Cup last term but he was omitted from the squad for the Spanish Super Cup last week.
The 26-year-old turned down a new deal at the Bernabeu and Real Madrid coach Carlo Ancelotti said he had bade farewell to players and staff on Sunday.
Di Maria's signing would provide a boost for Louis van Gaal, coach of Manchester United, who have taken only one point from their opening two games of the Premier League season.