The 35 million Liverpool forward was overlooked in favour of Manchester United striker Danny Welbeck for the 1-1 draw with France, but the two could be set to pair-up against Sweden.
Steven Gerrard and Scott Parker will stay in the centre of midfield having overcome exhaustion.
Wayne Rooney serves the last match of his two-game suspension.
Alex Oxlade-Chamberlain is set to miss out, with Ashley Young moving onto the left flank and Milner retaining his place on the right side of the midfield.
Hodgson wants his players to remain patient.
"One would hope people will be patient. I am satisfied with what I think we are achieving only three weeks into the job."
He added: "Maybe I can't satisfy everyone and other people would like to see more.
"I am realistic and pragmatic. Five, six or seven training sessions into the job we are making a fist of it.
"I am sure we will get better. Just a simple thing like the return of Wayne Rooney will make us into a stronger team and a bigger threat."
Sweden are expected to bring in West Brom centre-back Jonas Olsson and move Andreas Granqvist to right-back.
Johan Elmander is also set for a recall and should replace Markus Rosenberg in attack.
The Swedes lost their opening game of Group D to co-hosts Ukraine, but England are aware of how well organised they will be.
"They are organised as a result of years of work based on English coaching," said Hodgson, who began his managerial career in Sweden.
"Their major weapon is Ibrahimovic - he is one of the best strikers in European football."
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