Ronaldo's current contract had four years to run but United want to stave off Real Madrid.
A United source said: "This will be the biggest contract in the club's history. Given Ronaldo's achievements over the past two years, it's easy to understand why.
"There is no doubt he is the best player in the world and we want to make sure he is happy at United. There is only one place for him and that is Old Trafford."
Ronaldo's new deal will dwarf that of team-mate Wayne Rooney on £112,000 a week.