University of Utah infielder James Brooks was taken in the 20th round by the Washington Nationals.
Travis Huber, a pitcher who plays for Nebraska, was selected in the 23rd round by the Minnesota Twins. He is a former star at West Jordan High.
Southern Utah pitcher and former Murray High star Chase Rezac was taken in the 26th round by Cincinnati, and Utah Valley first basemen Goose Kallunki went to the San Diego Padres in the 27th round.
BYU had two pitchers selected: Chris Capper in the 26th round by the Arizona Diamondbacks and Austin Hall in the 33rd round by the Milwaukee Brewers.
Lail says that if the Yankees' signing bonus is sweet enough, he will likely sign with New York, rather than honor his scholarship commitment to Arizona. He has until Aug. 15 to decide.
"I've been talking to the Yankees and they said that they want me to start playing for them right away," said Lail, who was 9-3 for the Miners this season. "This was one of my favorite teams growing up, and it's a great thing to be drafted by them."