After the goalless Premier League draw between United and Chelsea, Shaw said he had heard Attwell tell Maguire that he didn't award a penalty for a handball on Callum Hudson-Odoi because a decision would cause "a lot of talk".
Attwell consulted the pitch-side monitor to judge whether Hudson-Odoi handled the ball inside United's box but did not award the penalty.
However, Sky Sports says Maguire has corrected Shaw's account of what was said between himself and Attwell when asked by United officials.
Manager Ole Gunnar Solskjaer was furious with the decision when speaking after the game.
"One hundred per cent," he said. "They're shouting it's handball for our player, but when you look at it on the video, it's taken two points away from us."