"It should not be the decision of one person," Miller said during an interview before the Democratic Party's annual pre-session luncheon. "I want everybody to weigh in on this decision."
The 90-day legislative session begins Wednesday.
Oaks was indicted on fraud charges near the end of last year's session, accused of using his official position to help a phony real estate development in exchange for thousands of dollars in bribes.
"This situation is an embarrassment to our state," state GOP chair Dirk Haire said early Tuesday. He demanded that Miller and Democratic Party Chair Kathleen Matthews "immediately take action to oust Senator Oaks, or explain why they think it is ok to protect public corruption by Democrats in the General Assembly."
The ethics panel could recommend that Oaks be reprimanded, censured or expelled, measures that would have to be approved by the full Senate.
Miller said that Oaks, who is awaiting trial later this year, "wants to have a way to prove his innocence," adding that it would be "unfair to jurors in the case, it would be unfair to Senator Oaks and everyone else" to "try him now in the papers."
After Oaks was indicted last year, Miller said he was "very disappointed" and "shocked" and had urged Oaks to turn himself in. On Tuesday, an aide to Miller said the Senate president believes that Oaks should resign.
Federal public defender Rebecca S. Talbott, who is representing Oaks, did not immediately return a call seeking comment.
Oaks was charged in federal court on April 7, a Friday. He shocked his colleagues the following Monday, April 10 — the final day of the session — when he walked into the Senate chamber and took his seat.
In November, Oaks was indicted on an additional count of obstruction of justice after being accused of trying to tip off someone under federal investigation while cooperating with the FBI.
Oaks has served in the General Assembly for 30 years. He lost his seat in the House of Delegates in the late 1980s after being convicted of stealing thousands of dollars from his campaign account. He regained his seat in 1994 and was appointed to the state Senate last year to replace a legislator who stepped down because of ill health.
He has shown no sign that he would consider resigning, despite a recent report in The Baltimore Sun that said Oaks had confessed to taking bribes and interfering with a federal investigation.
Federal investigators say Oaks misused his State House letterhead and introduced legislation to benefit the fake real estate project of a businessman who gave the lawmaker more than $15,000 in cash in 2016. The businessman was actually working for the FBI.
Oaks faces a maximum penalty of 20 years in prison, according to the office of the Maryland U.S. attorney.
Gov. Larry Hogan (R) said Tuesday that Oaks should have resigned after his indictment.
Hogan pushed last year for stronger ethics laws following a separate federal investigation that led to the arrests of Del. Michael Vaughn and former delegate William Campos, both Democrats from Prince George's County. They were charged with being involved in a wide-ranging bribery scheme.
On Tuesday, Hogan proposed legislation to limit lawmakers to two four-year terms, calling it the next step in an effort to root out corruption and stem partisan bickering. The legislation would not affect current officeholders. Maryland governors already face term limits.
Also last year, Hogan rescinded the appointment of Gary Brown Jr. to fill a vacancy in the House of Delegates after Brown was indicted on charges of making illegal donations to the political campaign of then-mayoral candidate Catherine Pugh (D) of Baltimore.