The Washington Post said the six-member group could unveil their deal as early as next Friday and set the stage for the first overhaul of immigration regulations in years.
"We have basic agreement on many of the core principles," Senate Majority Whip Richard J. Durbin (D-Ill.), a member of the group, said this week. "Now we have to draft it. It takes time."
The working group's deal may carry some political weight since its members include senior and high-profile lawmakers. The members are Republican Sens. John McCain, Marco Rubio and Lindsey Graham, and Democrats Durbin, Charles Schumer and Robert Menendez.
Details of the strategy were not immediately available, but the Post said the plan was expected to include normalizing the immigration status of illegal immigrants and allowing those without criminal records to obtain legal work permits.
Another potentially controversial aspect of the new move could be the role of President Obama's volatile healthcare reform plan. The Hill said Saturday the normalization of the status of millions of illegal immigrants could allow them to buy health insurance through the insurance exchanges to be set up under the Affordable Care Act.
Proponents say that could be a blessing for hospitals that currently treat scores of immigrants who are currently uninsured. It would also get more immigrant workers on the tax roles.
Critics, however, may also see it as opening the door for more people to seek government healthcare benefits.
The next step will on Capitol Hill where actual legislation will be parsed and debated by a sharply partisan Congress.
The Post said it remained to be seen if the overhaul would take the form of one massive bill or several smaller measures that could make it easier to digest.
"I doubt if there will be a macro, comprehensive bill," said Sen. Johnny Isakson, R-Ga. "Anytime a bill is more than 500 pages, people start getting suspicious. If it's 2,000 pages, they go berserk."