The Liverpool midfielder has been out of action since February with a groin injury although did make Southgate's final squad for the tournament, but it is doubtful that he will play in the game against Croatia on June 13.
The Three Lions boss said: "I don’t think it would be fair to rule him out of it but I think it’s clear to everyone how much football he’s missed.
"The timelines are getting more difficult with each training session he might miss. But I’m being very realistic about what’s possible here.
"It’s a decision we took (to select Henderson) because we have been able to take extra players and we feel he is such an important influence around the place.
"If we can get him close to being able to contribute on the pitch against Croatia that will be a real bonus at the moment."
Henderson could be replaced in the team by Jude Bellingham if he is not fit enough for the tournament and Southgate has no doubts about the Borussia Dortmund player, even if he is aged just 17.
Asked if Bellingham would start for England, the coach said: "The best way to answer that is to say he is not just here for the experience.
"You’ve seen what he is capable of, we’ve seen that for Borussia Dortmund especially in the Champions League.
"The whole group respect him, he has great humility around the camp but he competes in training like he’s been with them from day one which is a great mentality to have."