Rana had been sent to England for fresh scans after he was advised to take six weeks' rest and possibly undergo surgery that would rule him out of the four-Test series in England starting next month.
"I spoke to Rana and he said he is much better. The specialist in London has given him one week's time to show some improvement," Woolmer told Reuters.
"If there is improvement then he has an outside chance of making the tour. If not then apparently he has to go in for a surgery which would rule him out for the tour."
Pakistan have already lost fast bowler Shoaib Akhtar to a stress fracture of the ankle and he has not been picked in the squad for the four Test matches, the first of which starts at Lord's on July 13.
"Shoaib will have fresh scans and if he is allowed to resume bowling then he might accompany the squad to England and make a full recovery there," Woolmer said. The former England player said the selectors had not yet decided on a replacement for Rana.
Woolmer also praised the contribution made by former South African player Jonty Rhodes during his short stint as a fielding consultant before the tour of England.
"Rhodes has come up with very good ideas for our players and they have also enjoyed the drills and responded to him," he said.
"He has taught the players to do some things differently and effectively.
