But Chief Thomas Jackson and the city's mayor say the reports aren't true.
Under the proposed plan, after Jackson leaves, city leadership would ask the St. Louis County police chief to take over management of Ferguson's police force.
The announcement could come as soon as next week.
It would be one step in what local officials hope will help reduce tensions in the city as the public awaits a decision on whether the St. Louis County grand jury will bring charges against Officer Darren Wilson in the fatal shooting of Michael Brown.
"The animosity that existed in Ferguson were way before Mike Brown's shooting, justified or not. So, unfortunately, the leadership in the police department has to change," said CNN legal analyst Mark O' Mara. "And if he's sort of a sacrificial lamb to get this started, it's going to have to be. Ferguson's going to have to more forward. And it doesn't seem they can move forward with this police chief in place."
Jackson said Tuesday he is not being pushed out.
"Nobody in my chain of command has asked me to resign, nor have I been terminated," he said on the phone to CNN.
And Ferguson Mayor James Knowles said there is no plan in place for the police chief to step down.
When asked whether the federal government was pressuring the city to force out the police chief, he told CNN: "People have been saying that for months, I mean for him to step down. But we've stood by him this entire time. So there is no change on that."
The St. Louis suburb drew national attention after protests erupted following Wilson's shooting of Brown, an 18-year-old unarmed African-American.
Wilson, who is white, hasn't been charged in the case, though a grand jury is hearing evidence that could lead to an indictment.
CNN analyst Michael Smerconish think Jackson's removal, if true, is indication that the grand jury may decide not to indict the officer.
"To me this is all calibrated and intended to take the temperature down of the community," Smerconish said. "I'm absolutely convinced we're headed for no indictment in this case.
Jackson had faced criticism over his department's handling of the Brown shooting and the protests in its aftermath
"I've talked to a lot of people who have initially called for that and then changed their mind after having meetings and discussions about moving forward," he said. "Realistically, I'm going to stay here and see this through."
Speaking about his job and the fallout over the Brown shooting, he said, "This is mine, and I'm taking ownership of it."
Justice Department investigators are looking at the Ferguson Police Department's use of force, analyzing stops, searches and arrests and examining the treatment of individuals detained at Ferguson's city jail, U.S. Attorney General Eric Holder has said. That complicates plans expressed by some officials who want to dissolve the entire Ferguson Police Department and turn over law enforcement to county police.
In an interview with CNN last week, Holder said the Justice Department was looking at the leadership of the Police Department as part of its ongoing investigation of the department's practices.
"We have an ongoing -- having a practice investigation into the Ferguson Police Department. And we're looking at a whole variety of things, including the leadership of that department, the practices that the department engages in, the nature of the interaction between the department and the community that it is supposed to serve," Holder said. "So I think it's a little premature for me at this point to comment on the leadership of the Ferguson Police Department. That is certainly something that we are looking at."
Last month, Jackson released a video apology he said was directed at Brown's parents and the peaceful demonstrators who took to Ferguson's streets to protest the teen's death.
"The right of the people to peacefully assemble is what the police are here to protect. If anyone who was peacefully exercising that right is upset and angry, I feel responsible and I'm sorry," he said.
He also acknowledged that the incident had sparked a larger conversation about societal issues.
"Overnight I went from being a small-town police chief to being part of a conversation about racism, equality and the role of policing in that conversation. As chief of police, I want to be part of that conversation. I also want to be part of the solution," he said.
He conceded that Ferguson and the surrounding areas have "much work to do."
"For any mistakes I've made, I take full responsibility. It's an honor to serve the city of Ferguson and the people who live there. I look forward to working with you in the future to solve our problems, and once again, I deeply apologize to the Brown family," he said.
Later that day, he waded into the crowd at a protest and apologized again.
Some people seemed satisfied by his apologies. But not everyone was anxious to hear from him.
One man shouted into a bullhorn: "If you are not resigning tonight, go home."