"The government itself must remain strong," he said.
The bill to remove Naize will be among the first items considered by the council, which meets in the tribal capital of Window Rock. If passed, another bill sponsored by Shepherd would appoint a replacement.
Prosecutors have alleged that Naize and other tribal employees mainly current and former council delegates engaged in a scheme to divert money to their families that was intended for Navajos facing hardships. About 20 people face criminal charges or are accused of ethics violations in the investigation.
Naize declined to speak in detail about the case. His chief of staff, Jarvis Williams, said the financial assistance wasn't limited to people in the lowest income brackets.
Naize said he will plead not guilty to the 10 counts of bribery and a conspiracy charge at his arraignment in March.
Shepherd said his legislation is aimed at preserving the integrity of the speaker's post. He also said the charges could compromise the council's relationship with county, state and federal agencies.
"Do we continue to accept this type of action, or do we say no more?" Shepherd said.
Written comments submitted to the council on Shepherd's legislation overwhelmingly are in support of removing Naize as speaker before his term expires in January 2015. A two-thirds vote of the council is required for the legislation to pass.
Naize said he won't run this year for a seat on the council after serving 16 years.
Naize is part of the first group of 24 delegates who were elected to the council after Navajo voters reduced it from 88 members. He said it's important for the council under his leadership to build on goals to restore the public trust and to make the legislative process more transparent and accountable.
"A distraction is there, but (we) must understand that those have to continue what we have outlined from the beginning," he said.
The first day of council sessions generally is reserved to hear reports from the tribal president, council speaker and others.
The council also will take up a bill this week for an additional 2 percent sales tax on junk food. Proponents say it would curb health problems such as diabetes, while opponents say the proposed tax is too high and would be a burden.