Zaheer, who made a comeback to the Test team during the disastrous tours of South Africa and New Zealand after a long injury lay-off, failed to trouble the batsmen.
Although he bowled 51 overs and took a five-wicket haul in the second innings of the Wellington Test against New Zealand recently, he looked far from impressive.
"Can he survive five Test matches in England? I am not so sure," Dravid was quoted as saying by 'ESPNcricinfo'.
With 311 wickets in 92 Tests, Zaheer is the second most successful India seamer after Kapil Dev but his career has been plagued by injuries.
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Dravid said he would hate to see Zaheer end his career on a low.
"He has done a great job to get himself fit for these two series and to be fair, he has bowled well in patches, he has bowled consistently," said Dravid.
Talking about Indian spinners, Dravid said in the past also they had struggled in overseas conditions and people need to be patient with them.
"We will need to show some patience with our spinners, whether it is R Ashwin or whether it's (Ravindra) Jadeja, it's early days for both in international cricket," he said.
"I thought we were a little bit impatient with Ashwin. We haven't given him as much a run as I would like, so I think there is an opportunity for him to get back into the side and play a few more games. He will only learn if he play more games," insisted Dravid.