The skipper sustained an ankle injury in the closing stages of the 3-0 win over Cameroon, following a late tackle from Alexandra Engolo.
Houghton had opened the scoring with a superbly-placed indirect free-kick in the Round of 16 clash and Neville asserts Wednesday's training session will determine whether the skipper will be fit to participate in Thursday night's last eight tie.
The England boss also revealed Houghton's defensive partner Millie Bright may miss out, suffering from a virus, while Lucy Bronze is fully fit.
"Both are major doubts," he stated. "Steph Houghton because of the tackle.
"We're hoping she takes part in some of the training today - that's the key for Steph.
"Millie Bright has got a virus, which has been going through the camp. She's more of a doubt than Steph.
"We're going to give them until the last minute to be fit."
Previewing Thursday's game - a repeat of the 2015 Round of 16 encounter between the sides - Neville admitted his wariness of Norway, highlighting their key strengths as cause for concern.
"If we were able to pick our quarter-final opponents, I think the one we'd have said would be more difficult would be Norway," he added.
"They're a dangerous team, especially on the counter-attack, with lots of quality and speed. With their system, physicality and technical ability, they tick every box.
"They're probably the surprise team of the tournament because people have been focusing on the top ten teams in the world and they don't fall into that category.
"They're having fun and smiling. They've got a spirit and a togetherness with a tactical system, which is difficult to play against, and they look like they've for a cause.
"Maybe the fact that Ada Hegerberg didn't come has given them a cause: to win without their best player. It's always a good thing, having that 'siege mentality'.
"We're going to have to jump up 10 or 15% in performance level if we're going to be successful in this game and this tournament.
"It will be a really difficult game."