The council made the decision that the department could run effectively with the two lieutenants sharing administrative duties.
Kuhn, who has been on medical leave for several weeks, was unavailable for comment this morning on whether he plans to seek the chief position.
The issue over the police chief position has become a subject of several letters in this newspaper following comments in a newspaper story from Mayor Wayne Johnson, who said he would not support Graham for the chief position.
Johnson, a former member of the Police Department who worked under Graham, said he does not like the way Graham operates.
Johnson said this morning, "It's in the best interest of the city to find the best person for the position.
"After receiving all the applications and then going through the screening process, (Graham) may be the one chosen for the position, but we won't know that until we go through the process."
Graham said this morning he did not wish to comment on statements in the earlier story.
Graham said, "It has always been my ultimate goal to finally reach this apex in my career."
The Brawley City Council has shown signs of being split over the chief issue.
Councilman John Benson has said he supports advertising for a chief.
Council members Jo Shields and Toni Carrillo have said they are ready to support Graham or Kuhn should either be interested in the position.
Councilman Steve Vasquez has said he is open to advertising for the job, but he could support Graham or Kuhn for the job.
Graham and Kuhn have worked in the Police Department for about 30 years, both working their entire careers with the department.
Staff Writer Darren Simon can be reached at 337-4082.