Labour MP for Rhonda Chris Bryant signalled earlier this year that he would run.
Having served as shadow leader of the Commons between 2015 and 2016 and as a junior shadow minister under Ed Miliband, Bryant is said to have some support among Tory MPs.
Bryant is also among the favourites to take the job.
He told the House magazine that MPs were “battered and bruised enough” in parliament, adding: “So, the first thing for me is I will do everything in my power not to belittle or diminish or lecture MPs from the chair, but, insofar as it is possible, to respect every single person.”