The Croat claims that his young hotshot has similar mental qualities as Spurs' latest star.
Alli, 19, has been one of the stars of the Premier League season, netting seven goals and setting up another five in what has proven an exceptional first full campaign with Spurs.
The future also looks similarly bright for midfielder Oxford, who at the age of 16 impressed in the Hammers' 2-0 win at Arsenal on the opening day of the 2015-16 term.
Injuries to first-team players is expected to see Oxford - now 17 - given an extended run in the senior side over the coming weeks after a low-key last few months, but Bilic backs him to perform, stating that he is made of the same stuff which has helped Alli come to prominence.
“He is young, a kid, we shouldn’t forget that,” Bilic told a news conference, as quoted by London 24. “He needs a tap on the shoulder sometimes, but he is very calm, part of that generation that is young and brave and confident.
“He doesn’t think about mistakes. Like Dele Alli, it is very common with young players. You watch Alli on the pitch, every time he gets the ball he wants to pass forward.
He doesn’t want to go backwards or sideways and isn’t worried about mistakes. Even when he came on against us the other day.
"We know he [Oxford] is good, he knows he is good."
Oxford came off the bench to help United beat Spurs on Wednesday, combating striker Harry Kane relatively well in his 24 minutes on the field.
He could make his first league start this calendar year in Saturday's trip to Everton.