Van de Beek is on the verge of completing a £40.3 million move to United after he completed his medical on Monday.
The 23-year-old has held talks with Ole Gunnar Solskjaer last week and the midfielder has now agreed to a long-term contract worth just under £110,000 a week.
According to MailOnline, Van de Beek is likely to ask for the No.34 shirt at United in honour of Nouri.
Nouri played alongside Van de Beek at Ajax but suffered permanent brain damage after he collapsed during a friendly against Werder Bremen in July 2017.
The 23-year-old, who wore the No.34 shirt for the Dutch club, was in a coma for nearly three years and is now recovering at home.
Nouri also supported Van de Beek when the midfielder’s younger brother, Rody, was in hospital with a tumour in his back.
Rody has since recovered but in a youth-team game against PSV, Nouri wore a T-shirt which had a picture of Van de Beek’s younger brother above the words ‘strength’.
In an emotional interview about Nouri last year, Van de Beek said: ‘I find it hard to talk about, because I hold these things in.
‘When I’m sad, I pull back. I’ve never had the need for a psychologist, because I my friends and family are enough for me. They are always there for me and they listen to me when I need it. I’ve learned who is always there for me.
‘Appie was a super happy kid, that wasn’t focused on himself, but mostly on the people around him.
‘He was good for others, a great player and a great person. When he got older he visited prisons to get young people on the right path and point them to their opportunities.
‘And he took all the time in the world for people with illnesses and children with disabilities. I will always remember that.
‘I thought the most beautiful thing was that he did it out of the sight of camera’s and photographers.
‘When my brother Rody was ill, Appie showed a lot of interest as well. And he got pleasure out of taking his little sisters to school and picking them up, and buying presents for them. He did anything for his sweet family.
‘Obviously I don’t want things like that to happen to anybody, but it seems it always hits the good people.
‘Appie always wanted the best for everybody and he absolutely did not deserve this. It makes me feel powerless and angry.’
Several players who have also left Ajax, including Justin Kluivert and Joel Veltman, have also taken the No.34 shirt at their new clubs as a tribute to Nouri.