Gohmert's announcement came a day after fellow Republican Representative Ted Yoho of Florida said he might be willing to put his name up against Boehner, the Ohio Republican who is widely expected to retain the top job in the chamber when the full House votes on Tuesday.
"Ted is a good man for whom I could vote, but I have heard from many supporters and also friends in Congress who have urged me to put forward my name for Speaker as well to increase our chances of change," Gohmert said in a statement. "That is why I am also offering my name as a candidate for Speaker."
House Republicans voted in November to re-elect Boehner as speaker, a post he has held for four years.
Gohmert said voters made clear they wanted change in last November's congressional elections in which Republicans strengthened their grip on the House and won control of the Senate.
Criticizing Boehner's move last month to pass a $1.1 trillion government spending bill with support from some Democrats, Gohmert said the race for speaker was not about a particular candidate but "whether we keep the status quo or make the change the country demands."
Boehner spokesman Michael Steel said in a statement: "Rep. Boehner was selected as the House Republican Conference's choice for speaker in November, and he expects to be elected by the whole House this week.”