New Jersey could start taking bets on sporting events as soon as Saturday as state lawmakers rush to pass an updated bill — and Gov. Phil Murphy signs it into law.

The new bill — one that does not contain any “integrity fee” payable to sports leagues — is expected to be introduced on Monday.

MLB and the NBA have been meeting with lawmakers pushing for a small integrity fee attached to every sports bet placed. The leagues said the fee would help cover the cost of keeping the games on the up-and-up.

“There will not be any integrity fee,” Assemblyman Ralph Caputo (D-Belleville) told The Post, adding the Senate version will look the same as the Assembly’s. The lack of an integrity fee is a big loss for the leagues.

One lawmaker called the attempt by leagues to grab revenue from the fee “extortion.”

Casinos and racetracks in the state had originally hoped to start taking bets as early as two weeks after the Supreme Court on May 14 ruled that the national ban on sports betting was unconstitutional.

But that deadline was missed as bookmakers waited as lawmakers moved to update the law. The Senate and Assembly hope to have a bill on Murphy’s desk by Friday.

An earlier version of the Assembly bill included an integrity fee of $7.5 million, or 2.5 percent from each bookmaker taking a piece of the expected $10 billion in annual gross gaming revenue in the state, whichever is less.

“We can do our own oversight through the New Jersey Division of Gaming,” Caputo said.

Former State Sen. Ray Lesniak, who in 2008 filed the first lawsuit against the sports leagues to allow sports betting, told The Post there is “no way” there will be an integrity fee.