But asked whether he was open to challenging Rubio in a primary, West said he didn't believe such a bid would be "viable."
“I’m not looking to create disruption within our party. I don’t think it’s a viable option, right now," he said.
West had, earlier this year, said he'd run for Senate: "If I see people that are not taking our country down the right path, if I see people that are not standing up for the right type of principles and putting their own party politics before what is best for the United States of America."
Asked if he would rule out challenging Rubio, West responded, "Chirping ... chirping ... chirping."
Again Wednesday, he stopped short of ruling it out. But he sounded a less aggressive tone when asked about his intentions.
“I’m not saying what I will do or what I won’t do. But I’m not looking to be disruptive. I’m about the American team. I’m about doing whatever I can to help the Republican Party. But I’m going to stick to my principles," he said.
West was known during his time on Capitol Hill as a conservative bomb-thrower and still retains an enthusiastic following among conservatives nationwide. He lost to Democratic Rep. Patrick Murphy in one of the nation's most expensive and closest races last cycle.
Allen West: 'Of course' I'll run for Senate if Rubio runs for president
"If that became an open seat, of course I would run. I have a good statewide appeal, and a lot of people would like me to get back on Capitol Hill," West told the Tampa Bay Times Wednesday.