Outgoing Sen. Bob Bennett (R-Utah) said Friday he's privately discussed the prospect that Republicans would pursue their own version of the DREAM Act next year.

Bennett said he would vote for the immigration legislation, which gives immigrants who were illegally brought to the U.S. as children a conditional pathway to citizenship, if Senate Majority Leader Harry ReidHarry Mason ReidThe Hill's Morning Report - Presented by Tax March - CDC in limbo on J&J vax verdict; Rep. Brady retiring Biden to tap Erika Moritsugu as new Asian American and Pacific Islander liaison White House races clock to beat GOP attacks MORE (D-Nev.) brought it to the floor under the right conditions.

If that fails, the outgoing senator said, Republicans have privately discussed the prospects of writing and passing a version of the DREAM Act that could make its way through Congress.

"Now, I know a lot of my colleagues are not happy to vote for it, and I don't think the votes ... are there to pass it in this Congress," Bennett said in his final conference call with Utah reporters. "And as I've talked, particularly to my Republican friends, I've said we really need to do this. Their reaction has been to me, privately, 'You're right. We do really need to do it.'"

Democrats are hoping to bring up the House-passed version of the DREAM Act for a vote in the Senate in the closing days of the lame-duck Congress. Bennett has said he would vote for a standalone version of the bill but not for one that is wedded to many other provisions he doesn't prefer.

But time is running out on the Senate's legislative calendar, especially as Republicans have demanded that taxes be handled before any other issue. Because no final deal has been made, it might be difficult for Democrats to pass the legislation.

"We don't like the specifics coming out of the House ... but we agree that, once the Republicans control the House, the Republicans have the responsibility to write a bill that we would vote for and send it over," Bennett said of his conversation with fellow Republicans.

"And we, at least the Republican senators I've talked to, we think that if we get a DREAM Act worded the way we like, we will vote for it, and we want to do it early next year," he added. "It's my hope — I don't expect it — but it's my hope that we can do it this year. If not, it's my hope a little bit stronger that it can be taken care of next year."

Such a move could anger conservatives if the legislation doesn't substantially differ from the Democratic-led legislation this term. Conservative activists were riled by President George W. Bush's push for comprehensive immigration reform in 2007, which — like the DREAM Act — they called an "amnesty" bill.

Republican lawmakers' tensions with the base contributed to the kind of anger in the party base that led to primary challenges to Republican incumbents this cycle. One such primary ended Bennett's career, after Sen.-elect Mike LeeMichael (Mike) Shumway LeeBiden sparks bipartisan backlash on Afghanistan withdrawal  Hillicon Valley: Biden nominates former NSA deputy director to serve as cyber czar | Apple to send witness to Senate hearing after all | Biden pressed on semiconductor production amid shortage Apple to send witness to Senate hearing after pushback from Klobuchar, Lee MORE beat out Bennett for the Republican Senate nomination in Utah earlier this year.