GREEN BAY, Wis. -- Aaron Rodgers said he's ready for "a dogfight" now that Brett Favre is coming back to the Green Bay Packers.

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Rodgers has been named the Packers' starting quarterback, but the team failed to reach a deal with Favre that would keep him retired. The NFL is reinstating Favre, and he'll report to training camp Monday.

Favre could be on the field as early as Tuesday.

Rodgers said he'll compete with Favre for the starting job if that's what the team decides.

Coach Mike McCarthy said he wants to talk to Favre first before deciding whether there will be a competition. He said the team has made "no promises."

The Packers elevated Rodgers to the top of the depth chart, and McCarthy has insisted Rodgers would be his No. 1 signal-caller even if Favre returned. But now he says, "It's important we sit down and communicate."

Favre flew to Green Bay on Sunday night and a few hundred fans waited in a lightning storm to greet his plane.

He could still end up in another team's uniform. The Milwaukee Journal Sentinel reported on its Web site Sunday night that the Packers have had preliminary contact with the Minnesota Vikings on a potential trade.

Rodgers had a rough night in the Packers' annual "Family Night" scrimmage at Lambeau Field on Sunday night. A few boos were mixed in with enthusiastic cheers from the crowd of 56,600 when he was introduced.

Rodgers hit his first pass of the night to Donald Driver. But then he missed on his next six attempts, including several balls that seemed to bounce off receivers' hands. McCarthy said Rogers was "solid" even though the offense struggled.

Following the scrimmage, Rodgers said if there's a competition between him and Favre, it's not "going to be easy" and that he is ready for a "dogfight."