''I've seen him batting in the nets so things are going in the right direction,'' Mr Graveney told BBC Five Live.
''Michael Vaughan is a crucial part of our team and I haven't had any information to suggest that there's anything dramatic happening,'' he added.
The 31-year-old has not played since returning midway from the tour of India. He underwent a knee surgery after that and his recovery has been painfully slow.
However, Mr Graveny said the English cricket board is ready to wait as long as it takes for Vaughan's knee to heal.
''It's progressing. It's probably taking longer than people wanted it to but it's the right thing in terms of the bigger picture to show a bit of caution at this time,'' he said.
The chief selector said Vaughan himself was anxious to return to action.
''He's desperate to be back involved and I'd like to think we can give him as much space as possible,'' Mr Graveney added.