The person said there was agreement among representatives of all 32 clubs on what items needed to be resolved before any offer would be accepted. A second person, also speaking on condition of anonymity because the talks are supposed to be secret, said those players gave what was termed "conditional approval" of the proposal - as it stood Wednesday.
"We still have a lot of work to do," said Pro Bowl offensive lineman Tyson Clabo, who played for the Atlanta Falcons last season.
The meeting at the NFL Players Association headquarters lasted nearly 10 hours and included the group's executive committee and the team reps.
In Atlanta, where the owners' labor committee met, general counsel Jeff Pash said the sides would talk through the night in hopes of having a final agreement ready to go Thursday.
"It's obviously a complicated agreement, but I think both sides are at the point where they can close, they should close, and we should be in a position to take votes," Pash, the owners' lead negotiator, said following a five-hour session at a hotel near Atlanta's airport.
NFL Commissioner Roger Goodell joined the meeting of nine of the 10 members of the labor committee, which hoped to recommend a finalized proposal to all club owners, who are due there on Thursday.
Remaining issues are believed to include how to set aside three pending court cases: The players' antitrust lawsuit against the NFL in federal court in Minnesota; the TV networks case, in which players accused owners of setting up $4 billion in "lockout insurance," money that the league would receive even if there were no games played in 2011; and a collusion case, in which players said owners conspired to restrict salaries last offseason.
"I think that's the healthy outcome: to have a complete, comprehensive, global agreement that settles all the disputes and puts us on a path where we are going forward together as business partners, the way it should be, rather that going forward with one hand and fighting over something that should be in the past," Pash said.
Asked whether owners would consider approving an agreement Thursday, Carolina Panthers owner Jerry Richardson smiled and said: "I'm always ready for a vote."
New England Patriots owner Robert Kraft, who is on the labor committee, wasn't expected to participate because his wife, Myra, died Wednesday, at age 68, after a battle with cancer.
Earlier Wednesday, NFLPA president Kevin Mawae cautioned not to assume the lockout will be over by the weekend, saying that his group was "not tied" to a deadline for getting a deal done in the next 24 hours.
"We want to go back to work, but we will not agree to a deal unless it's the best deal for the players," Mawae said in the morning.
"Our goal today is to see what is on the table and discuss outlying issues," he said. "The players are not tied to a July 21 timeline. Our timeline is that which gives us the best deal for the players - today, tomorrow or whatever it might be."
If the four-month lockout - the NFL's first work stoppage since 1987 - is going to end in time to keep the preseason completely intact, the players and owners almost certainly must ratify the deal by Thursday. The St. Louis Rams and Chicago Bears are scheduled to open the preseason Aug. 7 in the Hall of Fame game.
Asked whether that exhibition game will be played, Pash replied: "We'll see. It's getting tight. It would be pretty challenging. That's one of the things we'll have to focus on."
If owners do vote Thursday, at least 24 would need to OK the deal. If it's passed by both sides, team executives would be schooled later that day and Friday in Atlanta in the guidelines and how to apply them; topics would include the 2011 NFL calendar, rookie salary system and new free agency rules.
Ten players - including quarterbacks Tom Brady, Peyton Manning and Drew Brees, Chargers receiver Vincent Jackson and Patriots guard Logan Mankins - filed their antitrust suit March 11. That was the day the country's most popular sports league was thrown into limbo: Negotiations broke off, the old collective bargaining agreement expired, and the union said it was dissolving itself and becoming a trade association. That meant players no longer were protected under labor law but could pursue their cause in court under antitrust law.
The owners locked out players hours later.
"Obviously, there's the litigation with the named plaintiffs, and I am not familiar with the whole legal part of it. ... But at the end of the day," Mawae said, "the deal we are working on is the deal that's best for all the players in the NFL, and not just four guys."
AP National Writer Paul Newberry and AP Sports Writer Charles Odum in College Park, Ga., contributed to this to report.