"I hope negotiations will continue over the upcoming break to reach a bipartisan compromise on background checks, and I am hopeful that they will succeed," the Nevada Democrat said as he formally moved a package of gun-related bills onto the legislative calendar late Thursday.
"If a compromise is reached, I am open to including it in the base bill," he said.
"But I want to be clear -- in order to be effective, any bill that passes the Senate must include background checks," Reid said.
The expansion of background checks has been a central point of President Barack Obama's gun-violence prevention plan.
A compromise plan being worked out between Sen. Chuck Schumer, D-N.Y., and Sen. Tom Coburn, R-Okla., hit some speed bumps and Coburn pulled out after disagreeing with Schumer that private sales must include records similar to those kept by gun stores.
Recent surveys have found strong public support for requiring background checks for private sales, including those at gun shows and over the Internet.
The package to be debated in the Senate next month also will include stricter federal criminal laws for gun trafficking and provisions to improve school safety, Reid said.
While it will not include a ban on assault weapons, Reid said proposals to ban such weapons and high-capacity magazines could be offered as bill amendments.