May lasted just eight minutes of the 26-24 defeat by France in Paris before a broken nose ended his match and could see him ruled out of the trip to Murrayfield.
"Jonny suffered a fracture to his nose against France and will see a specialist on Monday for further assessment," read a statement issued by the Rugby Football Union.
"A decision on his availability for selection against Scotland will be made following that examination."
Should May fail to recover in time, Anthony Watson is likely to make his debut. Another option would see Mike Brown move to the wing and Alex Goode start at full-back.
Any lingering doubt over the fitness of lock Courtney Lawes was removed when it was revealed he had escaped structural damage to his cheekbone at the Stade de France, suffering only bruising.
Head coach Stuart Lancaster has urged England to draw inspiration from Wales' successful title defence last year in their own quest for Six Nations glory.
"Wales lost in the first game and won the Championship, don't forget that. That's what I told my players after the game," he said.
"France will be a tough side to beat, but Championships aren't won in the first round.
"We're disappointed to have lost and that's probably a reflection of where we are in terms of our expectation."
France were installed as favourites to relieve Wales of their crown after a late converted try, brilliantly finished by the cunning of Gael Fickou, sent England spinning to an agonising defeat.
"It will be difficult to pick the players up initially, but I'm confident of the impact it will have when I show them the tape of the game," Lancaster said.
"We showed great character, but the skill and execution and lines of running were also good.
"We'll take plenty of positives from that and we'll be able to get them in the right place because clearly Scotland away is a massive game."
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