On Saturday, Texas Republican Sen. Ted Cruz said he would object to the certification of Electoral College votes on Wednesday.
Pres. Elect Joe Biden won the race in November.
Trump and a number of his Republican allies have refused to accept the results.
Business Insider reports the GOP have used baseless claims of widespread voter fraud.
A number of other senators are expected to join Cruz, according to Axios.
Sen. Josh Hawley of Missouri has already said he planned to object to the certification next week.
Fox News reports that Hawley's effort is separate.