The winger was missing at the weekend.
The Star understands he was due to have a scan in Leeds on Friday, but a motorway closure meant he missed the appointment. It's been postponed until Monday.
At worst, Sheffield would have to place him on the reserve list and bring another man in. But finding like-for-like would be impossible.
Sheffield Wednesday boss and chairman unhappy after attackers leave for Premier League
Sheffield Wednesday ‘obviously huge’ but Charlton Athletic boss makes Owls statement
What Darren Moore had to say after Sheffield Wednesday's win over Charlton Athletic
The moment that changed the game and a star man rises – How Sheffield Wednesday battled their way past Charlton Athletic
Sheffield United: Boss's vow over £40m strike pair as Oli McBurnie enters make or break season
Vallerand has 49 points from 31 games and been described at the League's top player by his coach. His type do not frequently come on the market.
Sunday's epic match started with both sides bristling with aggression, none more than starting line-up winger Tomasso Traversa, who dropped the gloves with bigger opponent Riley Brandt, after 12 minutes.
After that, the action remained tense and at mesmerising pace.
Cardiff, who had demolished Guildford Flames 6-2 on Saturday with Cole Sanford staking a hat-trick, had the clearest chance of the first period.
Sanford thought he'd scored again, but his shot hit Barry Brust's post and stayed out.
Justin Hodgman, Robert Dowd and John Armstrong had half-chances, none clean enough to get past netminder Mac Carruth.
The Cardiff 'keeper was the reason why Sheffield couldn't secure a lead worthy of their second period domination.
Passes from Vojtech Polak annd Brandon Whistle set up Matias Sointu and Evan Mosey respectively but they couldn't outfox him.
The American picked two stinging shots out of the air with almost arrogant assurance.
Steelers really missed Vallerand's contribution on two power plays. And the home fans may have wondered if they'd pay for not tucking their chances away.
They did have another decent fight to warm a February afternoon though, Robert Dowd retaliating to a Jake Coughler crosscheck with some nice right hands.
But Devils again hit the post - it was anybody's game.
They opened the scoring through Coughler, on a disputed power play awarded against John Armstrong.
Sheffield upped their workrate. Hodgman hit the outside of the post before his side equalised on the power play, Dowd's shot bouncing to Matias Sointu to backhand home.
Tommaso then got the goal he deserved with a looping effort over Carruth at 51:53.
But the Welsh were far from done. Trevor Cox made it 2-2 at 58:10.
Carruth stopped a one-on-one with Dowd in overtime and Sheffield came off second best in the penalty shootout, with Cox scoring the winner.
Steelers at least ended with an overtime point.
Sheffield used to dislike going to the cramped confines of Manchester Storm's Altrincham Rink...not any more.
Saturday's 7-2 thumping of Ryan Finnerty's team followed earlier 8-3 and 7-4 wins there.
The visitors enjoyed a 4-0 middle period.
They had seven different scorers on the sheet, Schulze, Mosey, Latal, Sointu, Eberle, Dowd and Polak.
The game ended prematurely with 11 minutes left due to illness suffered by a home spectator. He made a full recovery.