Naved sustained a groin injury while playing for Sussex earlier in the English season and there were fears surgery might be required.
But the 28-year-old has made encouraging progress in his recovery and Pakistan had planned to give him a fitness Test on Thursday morning before the start of the tourists' four-day warm-up match against England 'A'at Canterbury.
However, that try-out has been delayed until the weekend at the earliest.
And with Naved not expected to be hitting top pace in the nets until Monday or Tuesday, just days before the start of the first Test on July 13, Woolmer said there was no point jeopardising Naved's fitness for the four-Test series just so he could feature at Lord's.
"He is improving on a daily basis and we were going to give him a fitness test tomorrow. But we have put him back a little bit because we feel he is getting better," Woolmer said Wednesday.
"He won't be available for the first Test match but certainly he could be available after that," the former England batsman added.
"We were going to see how fit he really was and put him through it. But we have just knocked that back two or three days because the groin is getting better and we don't want to rush it too much.
"Maybe we will give him a few days and he will be even better."
Pakistan are already without injured quick Shoaib Akhtar and they had hoped Rana would lead their attack in the absence of the 'Rawalpindi Express'.
Naved had already demonstrated a liking for English conditions this season, taking 34 wickets at an average of 15 in five first-class matches.
Pakistan opened their Test preparations with a comfortable eight-wicket victory over Leicestershire, but are now set to face sterner opposition against a team led by Robert Key and including other England Test players from the past six months in Matthew Hoggard, Ian Bell and Alastair Cook.
"It's good we have this sort of competitive game before the first Test," added Woolmer, who will be on familiar ground this week having starred at Canterbury as a player for Kent in the 1970s and 1980s.
"When England came to us we had two A sides against them and that is the sort of competitive level you want."