Henderson, 26, captained England in their 0-0 draw in Slovenia last month when Rooney was dropped to the bench.
“I don’t think we can have just one captain,” Southgate said.
“We have several leaders. Too much responsibility has been on Wayne – we need to share that. Once you have a team of those leaders you can have a lot of success.”
Tottenham striker Harry Kane will not feature against Spain, having been released from the squad over the weekend as he recovers from injury.
The 23-year-old damaged an ankle against Sunderland on 18 September and only returned for 73 minutes of action against Arsenal on 6 November before joining up with the England squad.
He was an unused substitute for the 3-0 win over Scotland at Wembley.
Southampton left-back Ryan Bertrand also missed training on Monday and, with only 19 England outfield players available, 17-year-old Spurs midfielder Dylan Duncan made up the numbers.
“There’s any different number of ways we can approach the game,” said Southgate. “For me, it’s an opportunity to build on the way we are playing. It’s a great challenge in terms of a different style of game.
“It’s a game we have to get tactically right, the way we press and use the ball.
“We want to build on last few performances, which I think have improved the detail of how we want to play.
“I don’t want to make loads of changes. If we don’t keep some consistency then we are not building and are starting again almost.”