Negotiations were slow-moving until Thursday, but the Bengals made another push to add the veteran.
Harrison and former Miami Dolphins linebacker Karlos Dansby came to Cincinnati on April 11 to visit with Bengals officials.
Coach Marvin Lewis said Friday that the club planned to sign one or the other, but not both.
The team is trying to fill a linebacker spot left by Manny Lawson, a starter last year who signed with the Buffalo Bills during the offseason.
Last month, the 34-year-old Harrison refused to take a pay cut requested by the Steelers and was waived. He is due to make $6.57 million in 2013. The Steelers were not interested in re-signing him, even at a reduced rate.
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Linebacker Larry Grant has been suspended for the first four games of the 2013 season for violating the league's policy on performance-enhancing drugs, according to Comcast SportsNet Bay Area.
The unrestricted free agent is a four-year veteran who started three games for the San Francisco 49ers last season in place of injured Patrick Willis.
Originally a seventh-round pick of the 49ers in 2008, he played in 34 games for the St. Louis Rams over the next three seasons after being signed off San Francisco's practice squad.
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New York Jets quarterback Mark Sanchez has spoken out this week about the attention team-mate Tim Tebow received last season, saying the media circus was more intense last year than it was when the Jets made it to consecutive AFC Championship games in 2009 and 2010.
Sanchez insinuated that the Jets could have handled the situation better.
"I think part of that, too, is ESPN didn't necessarily sneak in overnight at our training camp. They had to get permission to go," Sanchez said on Fox Sports Radio in Los Angeles on Wednesday.
Sanchez said Tebow received more attention from the media than any other player he has been around.
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The New Orleans Saints have announced that running back Chris Ivory has signed their restricted free agent tender offer.
Ivory has been the subject of trade rumours and the signing could be a precursor to a potential move. Ivory only played in five games for the Saints last year, rushing for 217 yards with two touchdowns.
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The Seattle Seahawks have re-signed kicker Steven Hauschka. Hauschka joined Seattle after being claimed off waivers on September 4, 2011. He has made 49 of 57 field goals in his two years with Seattle.
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