Grassley spokeswoman Beth Levine said her office received the invitation for the Oval Office meeting and it was still "under consideration."
The White House invited both Grassley, who is the chairman of the Senate Judiciary Committee, and Sen. Patrick Leahy (D-VT), the committee's ranking Democrat, according to the report.
Not accepting the President's invitation would be a break in congressional protocol as similar meetings occurred before the Obama nominated Supreme Court Justices Elena Kagen and Sonia Sotomayor, according to the Register.
The Senate majority and minority leaders and Vice President Joe Biden also attended those previous meetings.
Republicans on the Judiciary Committee sent a letter to Majority Leader Mitch McConnell (R-KY) on Thursday saying they will not hold hearings for anyone Obama nominates.
Senate Minority Leader Harry Reid (D-NV) said Wednesday that Grassley’s silence was deafening.
“But Sen. Grassley has surrendered every pretense of independence,” Reid said. “The Senior Senator for Iowa won’t respond to a personal invitation from the President inviting him to the White House to discuss the vacancy. Think about that. The President of the U.S. calls a very senior senator here and (he) doesn’t even respond to the President. This is a sad day for one of the proudest committees in the U.S. Senate. So I ask, is this the legacy he wants?”