Shaw made the claims when discussing his pick for the club's best player.
"If Marcus Rashford had been fit for the whole campaign and hadn't suffered his injury, I think he would have won without any doubt at all," Shaw said.
"Rashy would be pushing for the best player of the season across the entire league because he was that good.
"He was on fire at times and gave the whole team a massive boost. It was the best and most confident I've seen him, so he's absolutely, definitely, a contender."