Durant is listed at 7-5, followed by Warriors point guard Stephen Curry at 8-5.
Cleveland's LeBron James, a three-time Finals MVP, is next at 2-1.
Warriors forward Draymond Green opened at 17-2, followed by Cavaliers point guard Kyrie Irving (10-1) and Cleveland forward Kevin Love (15-1).
While the Warriors already have secured their berth in the Finals, the Cavaliers still must finish off the Boston Celtics to advance. Boston hosts Cleveland in Game 5 on Thursday. The Cavaliers lead the best-of-seven series three games to one.
No Celtics were listed in the opening MVP odds. Boston is 1,000-1 to win the NBA title at the Westgate SuperBook.
William Hill, which operates the sportsbooks at 109 locations throughout Nevada, received approval from state gaming control on Wednesday to offer bets on the NBA Finals MVP. It's the first time Nevada books have been allowed to accept bets on the NBA Finals MVP.
"We are extremely excited to add the NBA Finals MVP Award to our wagering menu," William Hill director of trading Nick Bogdanovich said in a release. "With so many All-Stars on the court at the same time, this is a fantastic Finals to start offering it."
For decades, Nevada's regulated sportsbooks were prohibited from taking wagers on events that didn't take place on the field, court or ring, but gaming officials have been more lenient in recent years, allowing bets on the winner of the Heisman Trophy and on the NFL draft, for example.
William Hill also was granted permission to accept wagers on the NBA draft, and it will be posting proposition wagers next week, according to vice president of marketing Michael Grodsky.
On Wednesday, the sportsbook at Station Casinos in Las Vegas opened the Warriors as -220 favorites over the Cavaliers in a potential rematch of last year's Finals. Early action on Golden State pushed the odds up to -300.
The NBA Finals are slated to tip off June 1.
Opening odds to win NBA Finals MVP (odds courtesy of William Hill's Nevada sportsbook):
Kevin Durant 7-5
Stephen Curry 8-5
LeBron James 2-1
Draymond Green 17-2
Kyrie Irving 10-1
Kevin Love 15-1
Klay Thompson 25-1
Tristan Thompson 60-1
Kyle Korver 150-1
Andre Iguodala 300-1
Deron Williams 500-1
Iman Shumpert 500-1
Channing Frye 500-1
Patrick McCaw 500-1
David West 500-1
Shaun Livingston 500-1
Zaza Pachulia 1,000-1