WASHINGTON—Republicans reconciling House and Senate tax bills say they are narrowing their differences, putting a $1.4 trillion tax cut on track to be unveiled by Friday and passed by both chambers next week.

Tuesday evening, Senate Republicans were preparing to send their latest offer back to their House counterparts, in a negotiation that centered on whether to set the corporate tax rate at 21% or 22%, or to maintain a goal of cutting the tax to 20% from its present 35% level.

Negotiators were making movement on a number of other issues. For example, they were leaning toward adopting and refining a Senate-developed tax regime for pass-through businesses, which include partnerships, sole proprietorships and other businesses that pay taxes through individual returns.

As a way to address concerns of lawmakers from high-tax states hurt by repeal of state and local individual income-tax deductions, they were also talking about setting the top individual tax rate lower than the House’s 39.6% level or the Senate’s 38.5% level.

“The rates, both the business level, the corporate level and individual level, are issues that are in play,” said Sen. John Thune (R., S.D.), one of the conferees.

Related Video The big focus in Washington this week is going to be how fast can Congress begin to move to wrap up a tax bill. WSJ's Gerald F. Seib explains some factors standing in the way and how likely it is a bill will get passed by Christmas. Photo: Getty (Originally Published December 5, 2017)

Negotiators were leaning toward capping mortgage-interest deductions at loans of up to $750,000, according to GOP aides and lawmakers. That represented a middle ground between approaches taken by the House and the Senate.

“The House and Senate both had strengths in their bills and so we really are picking and blending those strengths,” said House Ways and Means Committee Chairman Kevin Brady (R., Texas), the chairman of the House-Senate conference established to iron out differences. “I’m just really pleased with the direction we’re going on this.”

The end-stage negotiations are tricky in part because efforts to lock in Republican votes with more generous tax rules risk driving up the cost of the bill beyond the $1.5 trillion limit that Republicans established months ago. Moreover lawmakers have varying priorities. Sen. Marco Rubio (R., Fla.), for example, had wanted a more generous child tax credit for low-income families than he got in the Senate bill.

If Congress doesn’t cut the corporate tax rate as much as planned and doesn’t sweeten the child tax credit, he said, “it would be a problem.”

Related Video The sacred cows of the tax code—including breaks for home mortgage interest and state and local taxes—are being challenged. WSJ's Richard Rubin explains.... with real cows. Photo/Illustration: Heather Seidel/The Wall Street Journal

Republicans are working to meet a self-imposed deadline of Christmas to pass legislation that cuts the corporate tax rate, lowers individual income-tax rates and shields more estates from paying taxes, and pays for the cuts in part by eliminating or trimming tax breaks.

The party hopes to wrap up the first year of Donald Trump’s presidency with a signature legislative win. It is working against polls showing that the tax plan is unpopular. The GOP also has new incentive to pass legislation quickly, after a Senate seat for Alabama was thrown into Democratic hands Tuesday night, leaving Republicans with a narrow 51-49 majority once Sen.-elect Doug Jones is sworn in.

“As soon as they do reach an agreement, we need to go vote, like within a nanosecond after that,” said Sen. John Kennedy (R., La.) “When you have your votes you go vote—you don’t wait around for somebody to go talk themselves out of it or somebody to get mad at somebody else.”

For pass-through entities, the center of gravity in the conversation had shifted toward relying on an approach taken by the Senate. The Senate voted to give owners of all pass-through businesses with up to $500,000 of income access to a 23% deduction from their income taxes.

Newsletter Sign-up Capital Journal Scoops, analysis and insights driving Washington from the WSJ's D.C. bureau. PREVIEW

Larger pass-through businesses would get the deduction, but accounting firms, law firms, architects, engineers, doctors, and other professional service providers would be excluded.

House Republicans said the Senate’s idea of a deduction was more workable than their approach of a new 25% rate for pass-through business owners, although House Republicans prefer their own limits on who can qualify.

“I think you could see elements of both—this simple deduction that the Senate has come up with and then some of the guardrails that the House has proffered to prevent abuse,” said Rep. Carlos Curbelo (R., Fla.), a member of the tax-writing House Ways and Means Committee.

The Republican and Democratic conferees will debate their ideas on Wednesday, when the conference committee holds its first formal meeting, though the real negotiations are happening behind closed doors in the exchange of offers between Republican House and Senate negotiators.

On Wednesday negotiators could also learn the cost of some of their ideas, given that the chief of staff of the Joint Committee on Taxation, which evaluates how much revenue could be lost or gained under each proposal, is expected to be in attendance.

Separately, Sen. Bob Corker (R., Tenn.), the only Senate Republican who voted against the bill, held out the possibility that he might support the final GOP tax plan. “I’ve been on the phone a lot with the administration and the Treasury,” Mr. Corker said. “I’m going through a process and I’ll be finished in a couple days.”

Write to Siobhan Hughes at siobhan.hughes@wsj.com and Richard Rubin at richard.rubin@wsj.com