Washington (CNN) The Senate could soon vote on additional sanctions on Russia, following months of angst among senators on both sides of the aisle who've wanted harsher US action against Russia for meddling in last year's presidential election.

Talks were underway Wednesday among Senate leaders to hash out an amendment to attach to a separate bill related to more sanctions on Iran, which the Senate is expected to vote on in the coming days.

Negotiators are angling for language that would get bipartisan support. The move would send a signal to President Donald Trump, who earlier this year suggested he would be open to lifting sanctions if Russia cooperated with the US in the fight against terrorism.

"I think he's going to get a clear message from Congress that we want tougher sanctions on Russia," said Sen. Ben Cardin, the top Democrat on the Senate foreign relations committee.

Cardin told reporters that a consensus hadn't been reached yet and members are still sorting out provisions from different bills that have already been introduced this year, including two by Cardin, who teamed up with Republican Sens. John McCain and Lindsey Graham.

The top members of the Senate banking committee -- Republican Sen. Mike Crapo and Democratic Sen. Sherrod Brown -- also announced a bipartisan proposal last week.

"What may be necessary is to have different options -- let members offer their amendments and let votes be where they may," Cardin said.

The senators were still trying to hammer out final language Wednesday afternoon on Russia sanctions that could be added to the Iran bill, according to Senate aides.

Among the provisions that have been introduced this year are calls to codify into law existing Obama-era sanctions against Russia, require Congressional authority for any decision to lift sanctions, and roll out additional sanctions in response to Russian interference in the election.

Sen. Bob Corker, chairman of the Senate foreign relations committee, has been hesitant to take up a Russia sanctions bill in his committee. But he said last month that he wanted to see progress with Russia or else he would move a sanctions measure.

Senate Foreign Relations Committee ranking member Sen. Ben Cardin (D-MD).

On Tuesday, Corker said he had a constructive conversation with Secretary of State Rex Tillerson on the issue, but he expected a sanctions measure to move this month.

"We plan to deal with Russia during this work period," Corker told reporters. "My guess is there will be a sanctions bill that deals with Russia during this work period."

Senate Majority Whip John Cornyn told reporters he expects the amendment will get bipartisan support and will be brought to the floor "pretty quick," saying it could be this week or early next week.

Furthermore, Senate Majority Leader Mitch McConnell announced Wednesday morning he anticipates amendments will be offered, saying he applauded the efforts to come up with bipartisan legislation.

On the Democratic side, Senate Minority Leader Chuck Schumer said Democrats have urged Republican leadership to incorporate the provisions previously outlined in the sanctions bills that have already been introduced this session.

"If we do nothing on Russia or we have a weak bill, we will not accomplish that goal and Mr. Putin will continue to do everything he is doing," Schumer said.

Trump suggested in January before he was inaugurated that he would be open to lifting sanctions on Russia if they helped the US fight terrorists, though he said he'd keep the sanctions in place for "at least a period of time."

"If you get along and if Russia is really helping us, why would anybody have sanctions if somebody's doing some really great things?" he said in an interview with the Wall Street Journal

The issue saw renewed attention after Yahoo News recently reported that Trump administration officials began developing plans to lift sanctions almost as soon as they took office.

Former State Department official Dan Fried, who was quoted in Yahoo's story, later clarified to CNN that he did not have first-hand knowledge that the Trump administration would attempt to unilaterally relax Russia sanctions, but did reach out to some members of Congress because he was concerned by rumors he had heard from other officials that there was a possibility.

US Ambassador to the United Nations Nikki Haley emphasized on Sunday the Trump administration has "stood strong" on the existing sanctions on Russia.

"We're going continue to call them out as we need to. At the same time, we are trying to see if we can have talks with them on how to better come in line in the Syrian conflict. We're working with them on counter-terrorism. But if we see Russia doing anything wrong, we're going to tell them," she said on CBS' "Face the Nation."