Republicans hold a slim majority over Democrats in the U.S. Senate.
"It's time to move on," Roe, R-Tennessee, insisted in a conference call with reporters.
Roe voted against a House resolution appointing the impeachment managers who will prosecute Trump in the U.S. Senate.
"I've spoken to several of my Senate colleagues, friends that I have on the other side," Roe said of the impeachment trial. "They plan to start next week. What that structure will look like, I don't know. Whether there will be witnesses called, I don't know. I certainly don't have a problem if they do. I certainly hope it is a more open process than the House had which was a complete closed process."
Roe pointed out the impeachment trial of former President Bill Clinton lasted about four weeks with witnesses who were interviewed in private.
"I suspect if witnesses are called, this will take three or four weeks," Roe predicted. "If I'm (Sens.) Bernie Sanders or Elizabeth Warren and I'm running for the presidency, this comes at an inconvenient time to say the least with the Iowa Caucus and New Hampshire primary happening at that time. It's a political problem for them."
Roe also addressed these questions:
Are you hopeful for a quick resolution in the Senate with this impeachment trial so business on Capitol Hill can move forward?
"The answer is yes. This needs to be fair to everybody. I think it needs to be done as quickly as possible so everyone can move on. What I hear at home is people don't understand how it's gotten to this. "
What do you think of the comments from U.S. Sen. Lamar Alexander on allowing witnesses and saying he would not vote to dismiss the case?
"We had a process that was so flawed in the House when Republicans were unable to subpoena anybody. Most of the work was done in secret. It was not a proper process. I think it will be fairer in the Senate. I think there could be a lot of witnesses, including the whistleblower, Col. Vindman, the ambassador to the U.N., the ambassador to Ukraine. You could have John Bolton called."
What do you think of Sen. Blackburn's assertion that the Democrat senators running for president should recuse themselves from voting?
"I can see where she's coming from. In any other trial, if they would have said 'this person is guilty you ought to impeach him,' there's no jury in the world he would get on ... they are not an impartial juror, that's for sure.”