A federal judge ordered monitoring of the controversial sheriff's office in December, in a finding that Arpaio was guilty of racial profiling in the detention of ethnic minorities.
The manner in which the monitor will function is one of 11 areas that remain unresolved in negotiations with the American Civil Liberties Union, The Arizona Republic reported Friday.
Tim Casey, the sheriff's attorney, said Arpaio remains opposed to a court-appointed monitor.
While the sheriff was "very receptive and cooperative," Casey said the ACLU's proposal for the monitor to review a deputy's performance was beyond the scope of the judge's order.
"This lawsuit was not about any malfeasance in internal-affairs matters," he said.
Because the sheriff is an elected official, the monitor's power "has to be consistent" with powers granted to the sheriff by the state constitution, the attorney said.
"Unlike a police chief, the monitor cannot have the ultimate veto," Casey added.
The sheriff has rejected an ACLU proposal for an advisory board. Casey said Arpaio fears the board will be used to remove his from office.