Democrats are seeking more information about Mueller's report on his Russian Federation investigation.
"A tentative date has been set for May 15 and we hope the Special Counsel will appear", Cicilline, said during his interview.
Cicilline later tweeted that "nothing has been agreed to yet".
House Democrats are eagerly seeking for Mueller to testify before the House Judiciary Committee, whose chairman, Rep. Jerrold Nadler of NY, said last week the committee was "firming up the date" for Mueller's testimony and hoping it would be May 15.
The Democratic-led House of Representatives Judiciary Committee appears closest to arranging for Mueller to testify, possibly as soon as May 15.
Spokespeople for the Justice Department and Mueller declined to comment on Cicilline's remarks, and Mueller's spokesman declined to comment on Trump's tweet.
Mueller was special counsel in the investigation of Russian involvement in the 2016 election.
"The White House has so far indicated they would not interfere with Mr. Mueller's attempts to testify", Cicilline added.
If the report shows what Trump claims it shows, then why would he not want Mueller to testify? "That's up to the attorney general, who I think has done a fantastic job".
Mueller's testimony will be the most hotly anticipated Capitol Hill must-see TV since last week's Senate hearing with Attorney General Bill Barr.
The calls for Mueller to testify grew following Barr's testimony last Wednesday before the Senate.
Regardless, Trump's tweet represented a hardening of his own position and seemed certain to infuriate Democrats already angered by administration moves to impede a series of congressional inquiries. Early last month, the top Republican on the Judiciary Committee, Rep. Douglas Collins, Ga., urged Nadler to invite Mueller to testify, writing in a letter to the chairman, "If you seek both transparency and for the American public to learn the full contours of the Special Counsel's investigation, public testimony from Special Counsel Mueller himself is undoubtedly the best way to accomplish this goal".
Mueller reported that Trump in mid-2017 ordered McGahn to have Mueller removed.
The attorney general has been widely criticized by Democrats and some conservatives for how he has handled the release of Mueller's findings. "They will testify. The American people deserve the truth", Schiff said. Now he's trying to silence Mueller. When a reporter asked him on Friday whether Mueller should testify, he replied, "I don't know".