Leonid Mironov, speaking on Studiya 1+1 channel, said that the tissue was still swollen in Shevchenko's troublesome knee which took two blows in the Group D loss to France and win over Sweden.
The 35-year-old veteran striker, 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.
Ukraine rely heavily on his attacking flair and his absence from the match against England, which they have to win in order to qualify for the quarter finals, would be a huge setback.
"Andriy Shevchenko's condition as of 23:00 lights-out last night was satisfactory. There is less fluid in his knee joint. But the knee tissue is still swollen and he cannot fully bend his knee joint," Mironov said.
"Today we'll hold a doctors' council to decide whether he can take part in evening training. We will firstly take into account the player's feelings and what he wants. Andriy will have the last word as he knows his knee better than anyone else," he said.
"This morning the chances that Shevchenko will play against England are fifty-fifty. I think that Andriy, with all his desire to prove to the country and the whole world that he is a real professional, will do his best to play," Mironov added.
Coach Oleg Blokhin was likely to give further details on Monday about Shevchenko's chances of being fit for the match.
If Shevchenko cannot play, Blokhin may bring in Serbian-born striker Marco Devic to partner Andriy Voronin in attack.
Shevchenko is Ukraine's record scorer with 48 goals and was European Footballer of the Year in 2004.
He scored 175 goals for Milan between 1999 and 2006, winning the Champions League in 2003, but a move to Chelsea proved disappointing. He returned to Dynamo Kiev, where he started his career, in 2009 after a loan spell back at Milan.
Apart from his skill and experience, he is regarded as an inspirational figure whose mere presence on the field can get the best out of his team-mates.
