Luke Shaw claimed referee Stuart Attwell told Manchester United captain Harry Maguire that giving a penalty in Sunday's draw with Chelsea would have "caused a lot of talk".
The Red Devils saw their unbeaten Premier League run away from home stretch to 20 matches following a 0-0 stalemate at Stamford Bridge.
In the first half, Attwell checked on the pitchside monitor to see if a penalty should have been awarded to United when a bouncing ball struck the raised hand of Callum Hudson-Odoi, who was tussling with Mason Greenwood.
The official stuck with his initial decision not to give the spot-kick and, according to Shaw, he indicated to Maguire that changing his mind could have caused controversy.
"At the time I saw a handball and didn't know if it was Mason or Callum," Shaw told Sky Sports.
"I didn't know it was a potential check and that they needed to stop [the game] if it wasn't going to be a pen.
"But I heard the ref say to H [Maguire]: 'If I give a pen, it's going to cause a lot of talk after'. H was told it was a pen by VAR, but I'm not going to moan."
Speaking on Sky Sports, former United captain Gary Neville said the penalty would have been given before the guidance on handball incidents in the box changed in the Premier League earlier this season.
"There's no doubt earlier in the season that this would have been a penalty," he said. "Hudson-Odoi's panic is the fact that his arm shouldn't be there. I think it is a penalty."
However, Chelsea boss Thomas Tuchel said awarding a penalty would have been nonsensical as the ball also struck Greenwood's arm, though it hit the Man United forward second.
"How can this be a VAR intervention? The player in red plays the ball with the hand and then we are checking for a penalty? Why does the referee have to see this?" he said.
"I've seen it on the iPad, I don't understand why the referee has to check it but I'm glad it was no penalty. That would make it even worse."
The draw saw United move a point above Leicester in second in the table, although leaders Manchester City are 12 points clear.