An NHL source told ESPN.com's Pierre LeBrun that Clowe has been offered an in-person hearing at which the league will determine how much time he has to sit after leaving the bench to take on Chicago's Andrew Shaw late in Friday's game against the Blackhawks.
Shaw had just hit San Jose forward Joe Pavelski near the Sharks bench in the final seconds of Chicago's 2-1 win. He received a roughing minor and game misconduct.
Clowe sat out Saturday night's game against the Stars because of the incident and is facing a possible 10-game suspension for leaving the bench illegally.
Information from ESPN.com's Pierre LeBrun was used in this report.