The NFL said in a statement Sunday night that in the last week, lawyers for Walsh and the league have made "substantial progress toward an agreement that will allow Mr. Walsh to be interviewed."
"Both sides are optimistic that any remaining issues can be addressed successfully and they are committed to reaching a full agreement as promptly as possible," the statement added.
Walsh, a golf pro in Hawaii, has been seeking protection from lawsuits and other legal action, whether by the Patriots or other parties. The two sides have been negotiating for almost a month after reports surfaced just before the Super Bowl that Walsh videotaped a walkthrough practice of the St. Louis Rams before the 2002 title game. It was won by the Patriots 20-17 over the Rams, who were favored by more than two touchdowns.
Walsh's lawyer, Michael N. Levy of the Washington firm of McKee Nelson, confirmed Sunday night that an agreement was near.
"I have consistently asked the NFL to provide appropriate legal protections for Mr. Walsh," Levy said in an e-mail to The Associated Press.
"In recent discussions I have had with the league's lawyer, we have made substantial progress toward this end, and I am hopeful that we will be able to craft an agreement with the necessary legal protections so Mr. Walsh can come forward with the truth."
NFL commissioner Roger Goodell has said Walsh was not interviewed as part of the league's investigation into "Spygate," which involved the league confiscating tapes from a Patriots employee who recorded the New York Jets' defensive signals from the sideline during the opening game of the 2007 season.
Six confiscated tapes and other documents pertaining to the Patriots' taping were subsequently destroyed by the league. Goodell has defended the destruction of the tapes.
As a result of that investigation, New England coach Bill Belichick was fined $500,000 and the team was fined $250,000 and forfeited its 2008 first-round draft choice. That pick would have been 31st overall, but New England still has the seventh overall pick, obtained in a trade with San Francisco last year.
Goodell has also met with Sen. Arlen Specter, R-Pa., who asked pointed questions about taping of both the Pittsburgh Steelers and Philadelphia Eagles. The Patriots beat the Eagles in the 2005 Super Bowl and the Steelers in two AFC championship games.
"As commissioner Goodell has repeatedly emphasized, `Nobody wants to hear from Matt Walsh more than the National Football League,' NFL spokesman Greg Aiello said Sunday night.
In addition to the negotiations over Walsh's testimony, Willie Gary, who played in that game for the Rams, filed suit in New Orleans last month accusing the Patriots of fraud, unfair trade practices and engaging in a "pattern of racketeering." Three fans joined in the suit.
Specter subsequently said that his interest might be covered by that suit.
"I think now that the lawsuits have been started, that I got the ball rolling, and the plaintiffs' lawyers are picking it up," he said.