The trainer has confirmed that the Manchester United striker is under consideration to take the armband for his country for their remaining fixtures at the European championship
The Manchester United talisman will return to international action in England’s Group D decider with Ukraine following a two-match ban.
Rooney is expected to be placed alongside Danny Welbeck or Andy Carroll when they take on the tournament’s co-hosts on Tuesday evening.
"We haven't designated one yet but he [Rooney] is very much a candidate. Quite frankly, with him not being available we haven't really felt the necessity before now to decide on that," Hodgson told Sky Sports.
"But we are very much considering him for that position, yes."
Rooney himself admitted that he is happy with the way Hodgson is managing the Three Lions and stated that he feels comfortable under his new manager.
"It feels more like a club team now, rather than an international team," said Rooney.
"Everyone gets on with each other and there's a lot of trust between the players and the coaching staff, and everyone's happy.
"You only have to go to the hotel to see the lads. You've got [Manchester] City players playing snooker with United players. Everyone's mixing, everyone's getting on well and there's a good chemistry between the lads.
"At the minute, it's certainly the most comfortable I think the team have been off the pitch since I've been in the squad."