Sources involved in the negotiations say a deal could include provisions affecting border security and sanctions against employers of illegal workers, the Christian Science Monitor reported Friday.
The deal reportedly would also include a path to legal status for illegal immigrants currently in the United States, but the path may not extend all the way to full citizenship.
Lawmakers from both major parties say a failure to reach a deal by next week's deadline could put immigration issues off the table until after the 2008 election.
"This is the best chance the country has to repair a broken immigration system," said Sen. Lindsey Graham, R-S.C, who is urging Reid to extend the deadline. "If this moment passes, I don't know when we do it."
However, many conservative Republicans say they will reject any legislation that offers "amnesty" to illegal immigrants.
"We are here today to send a signal to the Senate leadership ... that if they do put forward their amnesty plan, then we will call it for what it is. And that is amnesty," said Rep. Lamar Smith, R-Texas.