The contracted Savage - an emergency for Hawthorn's Grand Final side - is seeking to be traded, with the Hawks' approval.
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As the Gillette AFL Exchange Period opens, Carlton, Melbourne, West Coast and St Kilda have expressed interest in the 22-year-old.
"It's been a really testing year fo r Shane, not just on the field but off the field. He's had some personal issues," Savage's manager Tim Hazell told Melbourne radio station SEN on Monday morning.
"He's been there for five years, played some really consistent football, but he probably hasn’t been in the 22 week in, week out. He's always been the one to be the sub or fall out of the side.
"He's just looking to revamp his career, and a fresh start might be exactly what he needs."
If a trade isn’t done, Savage could remain a Hawk.
"The beauty about Hawthorn – and I think (a reason) why they’re so successful on the field is how successful they are off the field – with (coach Alastair) Clarkson and (head of coaching and development) Chris Fagan saying, 'Go and seek out some other opportunities. If it doesn’t happen, then you come back and we'll give you a big hug and get you back into a positive mindset. It's been easy. It's quite rare," Hazell said.
Savage would be an attractive proposition to clubs looking for young midfielders with around 50 games experience in a good system.
He has played 56 games, making his debut late in 2009 after being pick No.75 in the 2008 AFL National Draft.
Savage was a substitute in the 2012 Grand Final side and was selected as a sub in all three finals that year, but missed out on selection in the 2013 premiership team after playing 15 games for the year.
Savage had an up and down season this year, being a standout in some games and then dropping away in others. However, he is considered a player on the up.
He struggled to find a permanent starting position in the Hawks' star-studded midfield and often entered games as a substitute.
He earned three Brownlow votes for his performance against St Kilda in round 20 but tailed off after that and was dropped for the finals.
However, he was a brilliant performer for the Box Hill Hawks during the finals series, kicking five goals and getting 28 disposals in the preliminary final.
He was also a strong performer in the Grand Final, helping Box Hill to an upset defeat over Geelong's VFL side.
