The Mavericks, sources said, will grant that permission but have told the Rockets that they'd like to delay the interview until after Dallas' first-round series with Portland so as not to disrupt the team's playoff preparations.
Sources said that Casey is one of the more serious candidates on a long list of potential targets to replace Rick Adelman, which stems partly from the Rockets' high regard for Mavericks coach Rick Carlisle.
The Rockets announced Monday night that they and Adelman, whose contract expires June 30, had "mutually agreed to part ways."
"I'm shocked that we still have him here. He's that good," Carlisle said. "That situation will be addressed at the right time, but my level of respect for Dwane and what he's brought our team is extremely high."
Casey came to Dallas with Carlisle to run the Mavs' defense starting with the 2008-09 season after posting a record of 53-69 in 1½ seasons as head coach of the Minnesota Timberwolves.
The 54-year-old Casey has been waiting for second shot at a top job since being dismissed by Minnesota with a record of 20-20 during the 2006-07 season. He narrowly missed out on coaching jobs last summer with the Atlanta Hawks and Los Angeles Clippers and ranks as one of the league's most highly rated assistants.
The Houston Chronicle reported in Thursday's editions that the Rockets already have established contact with two other high-profile available coaches -- Mike Woodson and former Cavaliers coach/current ESPN NBA analyst Mike Brown -- and have interviews scheduled next week with former Mavericks assistant Mario Elie (now with Sacramento) and current Rockets assistant Jack Sikma.
Sources say that the Rockets will not rush their search, however, to allow for the possibility that candidates not currently available -- such as Orlando's Stan Van Gundy -- could suddenly hit the market as Adelman did, depending on what happens in the playoffs.
Other assistants whose teams are still in the playoffs, such as Boston's Lawrence Frank and San Antonio's Mike Budenholzer, also are expected to draw interest from the Rockets.
The Chronicle reported that Houston also has interest in longtime Lakers assistant Brian Shaw if Shaw is not chosen by Los Angeles to replace the outgoing Phil Jackson.
Senior writer Marc Stein covers the NBA for ESPN.com. ESPNDallas.com's Tim MacMahon contributed to this report.