Rooney will return to the team on Tuesday after completing his two-match suspension following his red card against Montenegro in October, and either his Manchester United team-mate Danny Welbeck or Liverpool striker Andy Carroll will lose his place in the starting line-up.
Carroll scored with a header and Welbeck cleverly flicked home the winner when England beat Sweden 3-2 on Friday which put them in sight of the quarter-finals.
"I have a very difficult choice because both have done so well, both in the training matches before we came to the tournament and in the tournament itself," Hodgson told a news conference.
"They have given me the classic manager's headache but it's the headache we all want really, because they are players in-form and competing for a place.
"But since I have made it clear to everybody that Wayne Rooney will start the game it's a decision that has to be made - and I will make it."
Hodgson added that he did not think Rooney's enforced absence from the tournament meant he would necessarily come out with all guns blazing, unaware of his responsibilities to give a disciplined team performance.
"We will remind him that what we require from him is a good team performance," he said. "We want him to help make us a better team to help us win the game," said the coach whose team will advance to the last eight without worrying about France's match against Sweden if they avoid defeat to Ukraine.
France and England have four points each, Ukraine three and eliminated Sweden none.
Captain Steven Gerrard said he was delighted about the return of 26-year-old Rooney who will win his 75th cap against Ukraine and has scored 28 goals for his country.
"Everyone knows what Wayne Rooney is all about and he certainly makes us more threatening going forward," Gerrard said. "I can see in his eyes he is itching to go out and perform and hopefully he will play really well tomorrow and be the difference.
"I am not going to tell him not to be fired up for this game, he is all about being aggressive in the right way.
"Obviously we need him on the pitch. He regrets his reaction [against Montenegro] and the suspension and I am sure he will behave himself and put in a good performance for the team."
Hodgson praised the ground staff at the Donbass Arena, saying the pitch was in good condition following the battering it took from the thunderstorm that halted Ukraine's match against France for 55 minutes on Friday.
After walking around the stadium with the players on Monday, but not training there, Hodgson said: "The conditions are OK, and the groundsmen have done remarkably well following what happened the other night."
There was an emotional moment at the start of the news conference when Hodgson and Gerrard paid tribute to and sent their personal condolences to the family of 40-year-old former Daily Star football correspondent Danny Fullbrook who died on Monday after a long battle against cancer.
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