WASHINGTON (CNN) -- House Judiciary Chairman John Conyers, D-Michigan, is considering asking his committee to grant former top Department of Justice official Monica Goodling immunity in return for her testimony on the U.S. attorney firings.

The committee is expected to meet Wednesday morning to vote on whether to offer Goodling immunity, but it remains unclear if enough Republicans on the committee will support the move. Two-thirds of the panel needs to approve an immunity offer.

It remains to be seen if Goodling will accept an immunity offered or if she will continue to invoke her 5th Amendment rights, which protects witnesses from self-incrimination, if asked to testify about her knowledge of the Justice Department's handling of the firings of eight U.S. prosecutors.

A judiciary committee staffer tells CNN the process of negotiating immunity is a lengthy process which could take weeks to work out.

Goodling was among the senior Justice Department officials who participated in meetings and e-mail exchanges about the planned dismissals. She went on paid leave as the controversy grew and officially resigned her post on April 6.