"Senator Flake is still reviewing the tax reform bill on its merits. How he votes on it will have nothing to do with the president," a spokesman for the senator said in an email.
That is contrary to an assertion made by Trump on Sunday in a post on Twitter.
"He'll be a NO on tax cuts because his political career anyway is 'toast.'," Trump wrote of Flake on Twitter.
Where individual Republican senators stand on the tax bill has become the focus of those trying to determine whether it will pass because Republicans control only 52 seats in the Senate.
More than two Republican defections would likely kill the bill. Wisconsin Senator Ron Johnson has already publicly stated he opposes the bill in its current form.
The House voted last week to approve the tax bill with no support from Democrats and 13 Republicans defecting.
Trump and Flake, both Republicans, have been critical of each other in recent months. Flake delivered a speech on the Senate floor in October during which he said Trump threatened the nation's democracy. In the same speech, Flake announced he would not be seeking re-election to the Senate next year when his term expires.
Trump has in turn been critical of Flake, saying he would not be able to win re-election.
On Saturday at an event in Arizona, Flake was overheard on a nearby microphone talking with Mesa Mayor John Giles about Trump.
"If we become the party of Roy Moore and Donald Trump, we are toast," Flake said, according to television station KNXV, whose microphone recorded him.
Moore, who is the Republican candidate for a Senate seat in Alabama, has faced sexual misconduct allegations, and Republican leaders in Congress have urged him to drop out of the Dec. 12 special election.
In his Twitter post on Sunday, Trump also suggested that Flake intentionally made those remarks in order to be heard.
"Sen. Jeff Flake(y), who is unelectable in the Great State of Arizona (quit race, anemic polls) was caught (purposely) on "mike" saying bad things about your favorite President," Trump wrote on Twitter.