Silas reportedly had his second interview for the job Friday. Houston's next step will be for team officials to consult with players about the candidates, according to Berman.
Silas, presently an assistant coach with the Dallas Mavericks, is the youngest of the trio. Either Van Gundy or Lucas would represent a step back in time for the Rockets; neither has been an NBA head coach in well over a decade.
Van Gundy coached the Rockets from 2003-07, while Lucas is currently Houston's player development coach. Lucas last ran an NBA bench in 2003 with the Cleveland Cavaliers.
Longtime Rockets general manager Daryl Morey resigned Thursday, leaving the team's coaching search in the hands of vice president of basketball operations Rafael Stone and club owner Tilman Fertitta.