Hodgson has two big selection issues to finalise for England’s meeting with the co-hosts – who need a win to reach the quarter-finals – in Donetsk on Tuesday.
He must choose between Walcott or fellow midfielder James Milner.He must also select either Danny Welbeck or Andy Carroll up front.
Welbeck looks certain to partner Manchester United team-mate Wayne Rooney as he returns from a two-match suspension to make his first appearance of Euro 2012.
Hodgson was lifted by Walcott recovering from a slight hamstring problem in training on Sunday and his performance as a substitute against Sweden, when he scored the equaliser and created Welbeck’s winner in a 3-2 victory, means he is now under serious consideration to start.
Meanwhile, Ukraine striker Andriy Shevchenko is a doubt, rated only 50-50 to start the fixture.
Shevchenko, 35, is struggling with a left knee problem.
He picked up the injury in the 2-1 win over Sweden , though he then played in the 2-0 defeat against France.
Ukraine must win at the Donbass Arena in Donetsk to qualify for the quarter-finals at the expense of England, while a draw will be enough to see Hodgson’s side through.
“It will be no easy task against the co-hosts, who need victory to sustain their own hopes of progression and will be backed by fervent and colourful support in the biggest match in Ukraine’s history”
Shevchenko, who missed training on Sunday, scored both Ukraine’s goals against Sweden.
Team doctor Leonid Myronov says the former Chelsea striker has a “50-50 chance” of featuring against England.
He said: “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.”
Ukraine midfielder Anatoliy Tymoshchuk said: “Shevchenko is a little bit injured, but I don’t think it is that bad.
“He is a big player of our team and we hope he can play. He is the goalscorer and it will be very good for us if he could play.”
Shevchenko’s fellow striker Andriy Voronin said: “It is the biggest game in the country’s history. For us it is a very important game, not just for the whole team but for the whole country.”