The congressman said as much on Sunday during an appearance on CNN's "State of the Union" show, just days after he announced he was leaving the Republican Party.
"I still wouldn't rule anything like that out, I believe I have to use my skills, my public influence, where it serves the country best. And I believe I have to defend the Constitution in whichever way that works best," Mr Amash told host Jake Tapper.
The Michigan congressman also said he has had concerns about the Republican Party for years before announcing he was leaving the group in an op-ed published in the Washington Post on Thursday, America's Independence Day.
He also said that he plans on running for re-election in his district, and that he does not anticipate having major problems with winning his seat again.
Mr Amash has been a vocal critic of Mr Trump's, and was first elected into office during the 2010 Tea Party wave, a backlash to Barack Obama's presidency that saw a group of particularly zealous conservatives pledging limited government elected. Mr Amash had helped found the Freedom Caucus that embodied that movement, before resigning from that group in June.
Following the op-ed, Mr Trump attacked Mr Amash as "one of the dumbest and most disloyal men in Congress" and "a total loser".
Mr Amash said on CNN that the comments prove his point about Mr Trump, and suggested that "most people understand that’s not how people are supposed to talk about other to each other."
"He’s really identified what I talk about in my op-ed. He thinks people owe loyalty to him, but people are elected to Congress with an oath to support and defend the Constitution, not an oath to support and defend one person, the president, who happens to be in your own party," Mr Amash said.
An independent presidential bid from Mr Amash could devastate Mr Trump's chances at re-election, especially if he is able to attract enough voters away from Mr Trump's Republican base to help ensure a comfortable victory for whichever Democrat wins their party's nomination next year.
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