Naved is a member of the Pakistan squad touring England and was initially diagnosed as having a serious groin problem that would require surgery and a recovery period of three months.
The Pakistan board sent him to England to consult a specialist and get treatment in a bid to make him available for the tour of four Tests and five One-day internationals.
''We have got positive news today from the specialist. He says that Rana has shown improvement and his groin is better,'' PCB director Abbas Zaidi told Reuters today.
''He has been given a further period of 15 days to rest and resume bowling again. We are hopeful now he can be considered for selection after the first Test,'' Zaidi said.
The first Test starts on July 13 at Lord's.
Naved, 28, has appeared in eight Tests and 45 One-dayers and was in outstanding form for Sussex before his injury.
Pakistan has already lost fast bowler Shoaib Akhtar for the Test series due to a ankle stress fracture.
Zaidi said Akhtar was undergoing rehabilitation in Lahore and chances were he could be considered for the One-dayers.