England named their final 23-man squad for Euro 2016 earlier this week, with Manchester United teenager Marcus Rashford making the cut as one of five strikers.
But Hodgson still has his starting XI for the opening match against Russia on June 11 to consider and says there are as many as five players fighting to seal a spot in that team.
"I know the players, I know what they can bring and we are capable of playing against Russia almost with two elevens," said the England manager.
"That might be a slight exaggeration but not far off, so headaches still exist in terms of the final XI.
"There will be at least four or five players who possibly deserve a place in the team and they are going to keep fighting for that place.
"But, anyway, I am also hoping we will go beyond the first three games, and to do that I shall need more than 11 players."
Asked if he would experiment with different options, he said: "The first two preparation games were good in that respect - I don't need to try anything out any more.
"I don't want to commit myself to a team against Russia in 10 days' time, but it will be a strong team against Portugal.
"Wayne Rooney will be the captain and will obviously play, but I am not prepared to give too much away in terms of the other players who will start."
Hodgson, though, has had the bulk of his starting team in mind for many months.
He continued: "I have been close for a long time, because these are players that I have worked with for a long period of time.
"If you take out Marcus Rashford, who really is a new boy on the block, there is no one in there whose game I don't know really well.
"If they perform anything like they are capable of we will be a tough team to beat."