The measure calls for background checks for all gun purchases except for those between close family members and some hunters, the aides said, adding the caveat addressed concerns of some conservatives.
Manchin and Toomey spokesmen wouldn't confirm any details, saying only that the senators were talking with colleagues about gun legislation.
Toomey -- a conservative with Tea Party ties who received an "A" rating from the National Rifle Association, indicating a sterling gun-rights voting record -- faces re-election in 2016 in a Democratic-leaning state, the Post said.
He is among a growing number of GOP senators now saying they'd be open to expanded background checks if a bipartisan deal could be worked out.
Manchin, a moderate Democrat who also has an "A" rating from the NRA, has expressed a strong desire for a gun-control deal since the Dec. 14 Sandy Hook Elementary School massacre that left 20 children and six educators dead in Newtown, Conn.
He has been negotiating with Sens. Chuck Schumer, D-N.Y., Mark Kirk, R-Ill., and Tom Coburn, R-Okla., over the deal's details, but talks were stalled amid Coburn's opposition to requiring gun owners to keep records of private gun sales -- a point Schumer insisted on.
Schumer said Sunday he and other Democrats were open to changing the background-check language if Manchin can strike a deal with Republicans.
"Please let us go to the floor," Schumer told CBS News' "Face the Nation."
"If we go to the floor, I'm still hopeful that what I call the sweet spot -- background checks -- can succeed."
Sen. John McCain, R-Ariz., appearing on the same program, said in response to a question he wouldn't commit to supporting background checks on gun purchases at gun shows until he saw the final proposal.
"It really depends on how they're carried out, how long, what the depth of it is," he said. "This is another reason why we need to go to the floor."
Gun-rights advocates argue the background-check system is broken and expanding it would become a government gun registry that threatens the rights of law-abiding citizens to own guns.
They also criticize President Barack Obama for what they say is an attempt to use the Newtown tragedy to advance a liberal gun-control agenda.
Obama was to fly Monday to Hartford, Conn., where a sweeping state gun control measure was passed and signed into law last week -- to deliver a speech on gun violence.
At the University of Hartford, Obama was expected to "continue asking the American people to join him in calling on Congress to pass common-sense measures to reduce gun violence," the White House said Sunday night.
He was expected to "speak, as he did at the State of the Union, of the obligations we have to children lost in Newtown and other victims of gun violence to act on these proposals," a White House official told the Post.
Vice President Joe Biden is to hold a gun-control event at the White House with law enforcement leaders Tuesday, while first lady Michelle Obama will return to Chicago Wednesday to speak about gun violence from the perspective of a mother.
At the same time, at least 13 Senate Republicans, led by Rand Paul of Kentucky, Mike Lee of Utah, Ted Cruz of Texas and Marco Rubio of Florida, planned to send a letter to Senate Majority Leader Harry Reid, D-Nev., Monday formally threatening to block any new gun legislation.
Aides say they expect additional GOP senators to sign on to the filibuster threat now that they are back in Washington after a two-week recess.