Both players left Ajax at the end of last season, with Ziyech joining Chelsea for £36 million, while Van de Beek made the move to United in a £35m deal.
Ziyech’s start at Stamford Bridge has been disrupted after he suffered a knee injury during a pre-season friendly against Brighton but the midfielder finally made his debut in Chelsea’s 3-3 draw with Southampton last Saturday.
Van de Beek, meanwhile, is yet to start a Premier League game this season and played just two minutes in United’s victory over Paris Saint-Germain in the Champions League this week.
But Ziyech has told his former Ajax teammate to be patient and is confident the 23-year-old will ‘bring quality’ to Ole Gunnar Solskjaer’s side.
‘We spoke in the beginning when he moved to Manchester,’ said Ziyech.
‘And last week we didn’t speak a lot, we didn’t speak about his situation.
‘I think he will need time as well.
‘He comes from a different country, a different style of play.
‘I know for sure it will take some time for him as well to get used to everything and then I know for sure he will bring quality to the squad over there.
‘For him the most important thing right now is to stay calm.’
Ziyech also stressed the importance of finding his own rhythm at Chelsea following his delayed start to the campaign.
‘If you think realistically, I’ve been out for a while. The season stopped last year for me a bit early, I didn’t play for a while,’ said the midfielder.
‘Like I said before, the injury came at an unlucky time.
‘I know it will take some time but for me it could be as soon as possible.
‘But it is what it is right now and for me it’s now most important to build again to come in with 100 per cent fitness and that’s what we’re working on right now.’