At least five Republicans have said they would join Democrats to impeach Trump for the second time.
Lawmakers are set to introduce the four-page legislation Monday, with voting mid-week.
The president claimed the network "panders" to the left by having "loser" Democratic lawmakers Eric Swalwell, David Cicilline and Pramila Jayapal on air.
Republicans are clamoring for a vote. Democrats are not.
A bill prohibiting sale or possession of the firearms was introduced months ago. It's co-sponsored by 200 Democrats.
Members of both parties agreed that action is needed to address the threat news publishers face from Big Tech.
The president said last week that he would let Attorney General William Barr decide the matter.
Rep. David Cicilline (D-R.I.) had said representatives for the special counsel signaled Mueller could appear before the panel on May 15.
Rep. David Cicilline says the Fox News host's claim about Michael Cohen is already crumbling.
Democrats will investigate monopolies, oversee the regulators and write new antitrust legislation.