The restricted free agent is poised to make an announcement about his future in the coming days, with speculation intensifying about his likely move to Greater Western Sydney.
Just two days after winning the flag, the Franklin scenario is overshadowing celebrations.
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Fellow forward Jarryd Roughead said at Melbourne Airport on Monday that Franklin hadn't discussed his big decision with teammates.
"It's a decision he has to make with his friends and family.
"It's been a long year, as we've all said, with what's happened, but at the end of the day we've just won a flag and that's all that matters."
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The Hawks are travelling to Tasmania in two groups, with the first contingent stopping in Hobart for a government reception late Monday morning.
Franklin wasn't on the flight to Hobart but the club said he would travel to Launceston later on the day for a function at which the entire premiership team will be presented on stage.
