Mangini, 2-11 in his first season with Cleveland, spent time with Holmgren during the 61-year-old's two-day visit with the Browns. Mangini described Holmgren's visit as a chance to get to know each other better. Mangini said they talked about the Browns and other aspects of this season but provided few details.
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Holmgren came to town at owner Randy Lerner's invitation. He left without an agreement to take over the Browns, who have had just two winning seasons since 1999.
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.
Holmgren has also said he's interested in a front-office position with the Seahawks, who, like the Browns, dismissed their general manager during the season.
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.
If Holmgren decided to take the Cleveland job, sources say Mangini's future would be in considerable jeopardy.
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.
Report: Cleveland Browns, Mike Holmgren meeting about front office positionNeymar interest grows