Sources told ESPN's Adam Schefter on Thursday that the contract is for one year.
Kendricks pleaded guilty last week to the charges. A sentencing hearing is set for Jan. 24.
Kendricks, who signed a one-year contract with the Browns in June after winning a Super Bowl last season with the Eagles, used tips from an acquaintance to make about $1.2 million in illegal profits on four major trading deals, federal prosecutors said.
NFL spokesman Brian McCarthy said Kendricks' legal situation is under review, and Kendricks is currently allowed to sign a contract and participate in NFL activities, including games.
Kendricks played weakside linebacker for the Eagles, who drafted him in the second round in 2012 one spot before Seattle chose Bobby Wagner. K.J. Wright, Seattle's starting weakside linebacker, is recovering from arthroscopic knee surgery and is not expected to play Monday night against Chicago. Wagner also didn't practice Thursday with what the team listed as a groin injury.
"He's running today," coach Pete Carroll said of Wright. "He felt pretty good. We'll see how he goes. He's going day-to-day. He ran yesterday, and he's working out again today so -- he hasn't done that yet, but he's making progress. He's feeling pretty good."
Rookie Shaquem Griffin started at weakside linebacker for Wright in Sunday's opener and split time there with Austin Calitro. Carroll's comments on Tuesday suggested that Calitro could see more playing time in Wright's absence after Griffin found himself out of position a few times against Denver.
"Austin did pretty well and Griff, he had some problems on some stuff," Carroll said. "There were some things that happened to him that wasn't quite as clean as we would have liked. He got fooled on a couple things, but he played hard and he played tough and all of that. It's just first game, trying to figure it out. Even through preseason, he's had a lot of reps, but stuff happened to him for the first time in this game that hadn't happened before and he didn't always see it the way he needed to.
"It's a difficult transition that he's making. It's a lot to do in a short amount of time. They had a nice offense, they did some nice stuff and he wasn't quite where he wanted to be at times. So we'll just keep going. We'll find out during the week how the guys play and how they do and how practice goes, and we'll see what we're going to do about play time."
The 5-foot-11, 240-pound Kendricks recorded a team-high eight tackles in last season's NFC Championship Game against Minnesota and had four in Philadelphia's Super Bowl win. Kendricks signed with Cleveland in the offseason, and the Browns said they made the decision to release him after learning more about his involvement in the trading scheme.
ESPN's Brady Henderson and The Associated Press contributed to this report.