"I think there are a lot of Democrats who feel that way," Schumer said on CNN's "State of the Union." "We'll have to discuss it as a caucus, but I would support that move."
Virginia Sen. Mark Warner, the top Democrat on the Senate intelligence committee, proposed the idea after President Donald Trump fired FBI Director James Comey last week.
Trump has yet to name his choice to replace Comey, for which interviews have taken place this weekend
, and the Justice Department thus far has declined to appoint a special prosecutor. Republicans leading Congress have also declined to compel a special prosecutor or create an independent investigative commission.
Acknowledging Democrats' limited influence in Congress, Schumer told anchor Jake Tapper, "The key here, of course, is getting some of our Republican colleagues to join us."
Schumer said the need for a special prosecutor is stronger after Trump fired Comey, who was leading the FBI's investigation into the collusion allegations. The New York Democrat called on Republicans to put an independent investigation over party loyalty, and referenced the Republican senator who said
of then-President Richard Nixon during the Watergate investigation: "What did the President know, and when did he know it?"
"Where is the Howard Baker of 2017?" Schumer asked.
Schumer listed his criteria for a new FBI director, saying that the nominee should not be a "partisan politician," and should have experience and a willingness to stand up to potential pressure.
CNN has reported
that Trump is considering several Republican lawmakers for the FBI post, in addition to other candidates.
Schumer said both he and Democrats on the Senate Judiciary Committee have asked for a "thorough, thorough" inspector general investigation into any interference with the Russia probe and called for public testimony from Comey.
The Democratic leader also repeated his call for Attorney General Jeff Sessions to resign, saying that Sessions' involvement
in Comey's firing might have violated his recusal
from the Russia investigation in early March and that he has asked the inspector general to look into Sessions' role in Comey's ouster.
"The actions of the last week make all the more reason that he should not be attorney general," Schumer said.
Trump dismissed Comey unexpectedly on Tuesday. On Friday, he raised eyebrows again by tweeting a warning
to the ousted FBI director that he "better hope that there are no 'tapes' of our conversations before he starts leaking to the press."
In his news briefing later that day, White House press secretary Sean Spicer declined repeatedly to explain what the tweet meant or address questions about whether there were recording devices in the Oval Office.
Schumer said Sunday that if Trump is taping conversations, he must either submit the tapes to investigators or, if no tapes exist, apologize for misleading people about the possibility.
"To destroy them would be a violation of law," Schumer said. "He should turn them over to Congress and to the investigators. If there are no tapes, he should apologize to both Jim Comey and the American people."