Holmgren arrived Monday after being invited by Browns owner Randy Lerner and was again at team headquarters in Berea on Tuesday, club spokesman Neal Gulkis said.
Gulkis said Holmgren was accompanied by his agent, Bob LaMonte.
It is not known if Holmgren has been offered a job by Lerner, who last month said he wanted to hire a "serious, credible leader" to run the team. In an e-mail to The Associated Press, Lerner suggested the sides were still talking but gave no specifics.
Sources tell ESPN senior NFL analyst Chris Mortensen that Holmgren is hoping to have his future clarified and secured by Christmas. He recently returned from a nine-day vacation to Mexico with his wife, Kathy, where the couple was believed to have discussed his potential options.
Even if the Browns reach an agreement with Holmgren, it's possible they may have to conduct further interviews to comply with the league's "Rooney Rule," which mandates that a team must interview at least one minority candidate before filling a front-office vacancy.
If Holmgren decided to take the Cleveland job, sources say the future of head coach Eric Mangini would be in considerable jeopardy. Mangini told WTAM that he met with Holmgren.
"I have a ton of respect for Mike, and we'll see where it goes," Mangini told the club's flagship radio station. "They are still in the early stages and everyone is getting to know each other."
The Browns are 2-11, have lost at least 10 games six of the past seven seasons and have made just one playoff appearance since returning to the league as an expansion team in 1999.
Holmgren's visit was first reported by the Akron Beacon Journal and WKNR-AM.
The 61-year-old Holmgren previously served as the Seahawks' general manager and has expressed interest about returning to the NFL.
He recently told a Seattle radio station he found the Browns' front-office job appealing.
"There's something in my personality, too, that taking on those types of projects, that kind of gets me going. But there's a lot of work to do," he said. "The important thing, going into any organization is that all of the principles, all of the decision-makers are pointed in the same direction, with the same motives, the same desires, and then you have a chance."
Holmgren spent 10 years with the Seahawks and seven with the Packers, leading Green Bay to a Super Bowl title in 1996. Seattle made the playoffs six times with Holmgren, including its only Super Bowl appearance when the Seahawks lost to the Pittsburgh Steelers to end the 2005 season.
Holmgren was believed to be interested in returning to the Seahawks. Last week he said he "absolutely" wanted to talk to Seahawks owner Paul Allen and chief executive Tod Leiweke about returning to the team, which relieved Holmgren of his GM duties after the 2002 season. Seattle is looking for a general manager following Tim Ruskell's resignation on Dec. 3 and Holmgren could be using the Browns as leverage to get a deal with his former team.
It's not known what impact the hiring of a football "czar" will have on Mangini's future. The Browns have struggled in Mangini's first season, which has included lopsided losses, players grumbling about practice methods and fines and the firing of general manager George Kokinis.
The Browns are coming off a 13-6 upset of Pittsburgh and play in Kansas City on Sunday.
Mangini has said he would be open to Lerner bringing in someone to oversee the team's personnel decisions. On Monday, Mangini said he and Lerner have not discussed the search for that person.
"That hasn't really been the focal point of our conversations," he said. "It's more a function of the things that we're trying to do week in and week out. We'll visit some more and I'm sure we'll see where that is."
Lerner recently hired Fred Nance as the team's general counsel. Nance was one of five finalists to succeed former NFL commissioner Paul Tagliabue.
Holmgren reportedly turned down an offer from Buffalo to coach the Bills, who fired coach Dick Jauron last month.
Information from The Associated Press was used in this report.