A person close to Allen told The Associated Press on Sunday that he will make his plans official in a video to be e-mailed Monday afternoon to longtime supporters.
The person was not authorized to pre-empt Allen's announcement and spoke on the condition of anonymity.
The 58-year-old Allen joins a Republican field with candidates already staking out positions to his right. Tea party activist Jamie Radtke has announced her intent to seek the GOP nomination.
Del. Bob Marshall, one of the General Assembly's most conservative members, is also considering another bid for the GOP Senate nomination.