Hodgson is expected to bring the Manchester United player straight back into his team tonight after suggesting his influence on the England side could be similiar to Pele's inspirational performances for Brazil in major tournaments.
Phil McNultyChief football writer, BBC Sport
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
"If you look back through the years, if you take Pele for example, he was capable of producing his very best football when it really mattered to help Brazil win World Cups,'' he told ITV.
"Let's hope that Wayne Rooney can start to do that for us on Tuesday night and then, if we win, who knows?
"If Wayne can produce his best, then he can help us keep going even further."
Rooney has endured disciplinary problems in an England shirt, having been shown the red card in the 2006 World Cup quarter-final defeat by Portugal for stamping on Ricardo Carvalho.
But Hodgson has backed Rooney and his team-mates to keep their cool as they face a Ukraine side enjoying home advantage.
He told BBC Sport: "We will talk about it. Our discipline in our four games [that Hodgson has been in charge] so far has been very good.
"We have picked up a few yellow cards and have been unlucky to get them.
"The players will be aware we are playing away from home and we have to be careful as sometimes emotions do boil over."
Hodgson is setting up his team with the aim of victory tonight, as he fears playing for a draw could be disastrous.
Hodgson said: "There is the obvious pitfall that you could be tempted into trying to shut up shop and drop deeper and deeper only to find that in the last minutes of the game your opponents get a lucky goal, get given a penalty or a wide free-kick gets deflected into your goal.
Rooney's goals at Euro 2004
"We will be trying to make sure we take the initiative, but Ukraine will be trying to do the [same] and that is what makes this a fascinating game of football."
Captain Steven Gerrard insists the team are looking no further than the game against co-hosts Ukraine.
"I am trying to force myself not to even talk about quarter-finals and get involved in it. It would be very disrespectful to the opposition," said the Liverpool midfielder.
"Ukraine are very dangerous and we have watched tapes of them. Their combination play in the middle and around the box is good.
"If I started talking about quarter-finals and we slipped up, I would never forgive myself. Let's deal with the quarter-finals and what to expect if we get there and not before."
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