The 35-year-old forward took part in a squad training session on Monday but Blokhin said the decision over his involvement in the crunch game would not be made until match day.
"Its very hard to say, I'm not a magician, you should ask the doctor - we have 24 hours, it's 50/50 I think," he said when asked to rate Shevchenko's chances.
The loss of Shevchenko would be a huge loss for Ukraine because not only is he the country's all-time top scorer but he is a key figure in the dressing room.
Blokhin, who eventually demanded reporters in the news conference stop asking questions about Shevchenko, said there was no doubt his team would be weakened if the former AC Milan forward was out.
"Our team doesn't have so many stars as the French, Spanish or Italian team, so his role his very big, especially in our attack.
"There probably isn't any other such striker in Ukraine and if he cannot play - it would be a big loss for us," he said.
Earlier, team doctor Leonid Mironov, speaking on Studiya 1+1 channel, said the tissue was still swollen in Shevchenko's knee which took two blows in the Group D loss to France and win over Sweden.
Shevchenko, who scored both goals in his side's 2-1 win over the Swedes, missed training on Sunday because he could not bend his knee joint properly, Mironov said.
The co-hosts must beat England to have a chance of reaching the quarter-finals.
Blokhin said the pressure was on Ukraine's opponents given their higher status in the game and greater expectations.
"They are one of the favourites, so the pressure is on them," he said.
"We have a more relaxed approach, we have nothing to lose, even if we don't get a great result, if we show fight on the pitch till last minute that will be no disgrace," he said.
"England are a good team, everyone says they are tired but I really don't see that.
"They have a style of play and play to a plan. I don't believe this talk about English not being among the top teams," he said.
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