Williams, who has two years remaining on a contract that pays him $1.9 million per season, has told the Cowboys he is contemplating retirement. He did not report to training camp July 17.
Alan Herman, Williams' agent who arrived in Dallas from New York on Monday morning, said he spent the entire day with Williams.
"Basically, everything is the same," Herman said. "He's still considering retirement. He was in a good mood. I think he misses the camaraderie of the guys, but I don't think he misses training camp. Financially, he doesn't need to play. It's whether he misses the game or not."
There was some sentiment in the Cowboys' organization that Williams would return to the club this week because the toughest stretch of training camp, including last week's trip to Tokyo, is over.
"It's a week-to-week situation," Herman said. "[Owner] Jerry [Jones] has taken the position that he's going to let him think it through. I respect that. Erik is not fooling around.
"We talked about a whole lot of issues, and I just don't think he knows definitively whether he wants to come back."
Jones has said Williams can take as long as he wants to decide his future. Jones has also said that he wouldn't mind Williams joining the team once the season starts, if that's when he decides to play.
Herman said he has not asked the Cowboys to restructure Williams' contract.
"He's got a contract with two years remaining on it and he understands that," Herman said. "My job is to go over all of the issues and let him know what his options are."
Without Williams, who has been to the Pro Bowl two of the past three seasons, the Cowboys moved Solomon Page from right guard to right tackle. Free agent signee Jorge Diaz is starting at right guard.
Awaiting trip's effects
The Cowboys resume training camp at Midwestern State University in Wichita Falls on Tuesday afternoon. It will take a while for the club to measure the effect of last week's trip to Tokyo for an exhibition against Atlanta.
This marked the 11th NFL preseason game in Tokyo. The pattern for the previous participants has been a good September followed by a sluggish finish.
The other teams that have played in Japan went 56-20 in September for a .737 winning percentage. That included a 3-0 start by the 1992 Cowboys, who won the Super Bowl.
Most teams could not keep up that pace. The clubs that traveled to Japan went 129-108-1 after September for a .545 winning percentage. That includes flame-outs such as Kansas City, which followed a 3-1 start with a 4-8 finish in 1998; and New Orleans, which faded to a final mark of 8-8 in 1993 after winning its first four games.
The trip to Tokyo gives the Cowboys an unwanted distinction for this season. They are scheduled for an NFL-high 31,020 air miles. Tennessee will have the fewest air miles at 8,498.
The Cowboys signed former Oklahoma tight end Rickey Brady to a one-year contract. Brady (6-4, 246), played last year in NFL Europe with the Scottish Claymores. The team also brought in Hurley Tarver for a workout and is expected to sign the safety Tuesday. ... Oakland coach Jon Gruden held veteran wide receiver Tim Brown out of Saturday's game against St. Louis to look at other players. Gruden said Brown, from Wilson High School, will dress for Sunday's exhibition game against the Cowboys at Texas Stadium, but his playing time has not been determined. ... Rookie Michael Wiley has led the Cowboys in rushing in each of the first two exhibitions. Wiley has 59 yards on 15 carries. ... Safety Izell Reese expects to return to practice this week. Reese has missed all but one practice because of a calf strain.
Staff Writer Gerry Fraley contributed to this report.