The bad behavior of Pittsburgh Steelers quarterback’ Ben Roethlisberger resulted Wednesday in a six-game suspension by the NFL and reportedly has triggered what once would have been unthinkable: The Steelers are testing the market to trade him.

According to an ESPN report, Pittsburgh has been contacting teams selecting in the top 10 of this year’s draft, which begins at 4:30 p.m. PDT Thursday, to gauge interest in the two-time Super Bowl winner. By Wednesday afternoon, the network reported the Steelers had talked to St. Louis, San Francisco, Oakland, Jacksonville, Seattle and Cleveland. The 49ers are the only club without a top-10 pick (13 and 17).

In a conference call with reporters, Steelers President Art Rooney II was vague on the subject but didn’t deny his team was shopping the quarterback, who last month was accused of sexually assaulting a 20-year-old college student in Georgia but will not face charges.

“As we’ve said before, we really can’t answer questions about trades, particularly this time of year,” Rooney said. “We go into every draft with the idea that we’re going to do anything we’ve got to do to make our team a better football team. We just have to stick with that and not discuss trades in advance.”

What’s clear is the league and the Steelers have all but run out of patience with Roethlisberger, who last year faced similar accusations by a woman in Nevada. That case also did not bring criminal charges. Since then, reports have swirled that there’s a pattern of bad off-field behavior by the quarterback who once was among the NFL’s most popular players.

Roethlisberger will be suspended without pay for six games -- losing $2.8 million in salary -- for violating the league’s personal-conduct policy, and he must undergo a “comprehensive behavioral evaluation by medical professionals,” the NFL said.

There is some flexibility to the suspension. It could be reduced to four games for good behavior after that behavioral evaluation has taken place, but Roethlisberger cannot attend any Steelers offseason activity until he completes the evaluation process.

“We’re trying to affect behavior here,” said NFL Commissioner Roger Goodell, who has a reputation for disciplining players who run afoul of league policies. “We’re trying to make people understand their responsibility, live up to that standard, avoid making mistakes and use good judgment.

“We’re trying to have early intervention so that we can avoid people having criminal activity, deal with the issues and try to get them straightened out so they can lead productive lives. And if they can be great NFL players, terrific.”

Rooney said the Steelers support Goodell’s decision and that the club was willing to suspend Roethlisberger if the league did not.

“We do have high standards here,” Rooney said. “But by the same token, we understand that we’re in the people business and people make mistakes. And when they do, we have to follow the procedures.”

So far, there’s no indication Roethlisberger plans to appeal the suspension. Rooney was part of the phone call Wednesday when Goodell informed Roethlisberger of the suspension.

“His intent here is to follow the program the commissioner sets out,” Rooney said. “It’s our hope and our expectation that that’s what he’s going to do.”

sam.farmer@latimes.com