Two of Wall Street's biggest stock exchanges want Brett Redfearn, the head of the SEC's Division of Trading and Markets, to be recused from an impending case's decision over their market data businesses.

The New York Stock Exchange and Nasdaq Inc. recently renewed their 2016 motion to kick-start oral arguments again in a case expected to come to a conclusion in October by way of the agency's five-person commission. Brought by the Securities Industry and Financial Markets Association, the case dates back roughly five years and could have far-ranging impacts for Intercontinental Exchange Inc.-owned New York Stock Exchange, Nasdaq and Cboe Global Markets Inc.

At the heart of the case lies exchanges' market data feeds. SIFMA has argued that exchanges charge broker/dealers unfair prices for their market data products, which market participants say they need to subscribe to in order to comply with regulations to achieve the best price for a client's order. In late 2017, SEC Chief Administrative Law Judge Brenda Murray backed a 2016 decision in the case, saying that the market data businesses of New York Stock Exchange and Nasdaq, the defendants, are subject to competitive forces. SIFMA then appealed the decision to the SEC's commissioners, who will make the ultimate ruling.

The New York Stock Exchange and Nasdaq are hoping they will soon have another chance to argue their side in the case. Market data fees have recently gained increased public scrutiny from a host of executives and some regulators, indicating to the exchanges that the SEC should allow for additional arguments.

In their motion, the exchanges also called out a second possible concern involving the role of Redfearn, whose division oversees the exchanges, in the case. Redfearn, a former JPMorgan Chase & Co. executive, was reportedly an outspoken critic of exchanges' market data businesses prior to joining the SEC.

But on top of that, the exchanges claim Redfearn also had a "substantial personal participation" in the crafting of SIFMA's legal strategy in the case before joining the SEC, based on a recent article from The Wall Street Journal. The exchanges, as a result, said the SEC's decision should be clear that Redfearn was recused from the proceeding.

A spokesperson for SIFMA did not respond to requests for comment, and an SEC representative declined to comment.