In comments made to Eurosport, Sutton argues the first British winner of the Tour should not defend his French title and instead target the Italian and Spanish double.
"For me I would like to see Brad go out of this sport, not that he won't as it stands already, but as a legend," said Sutton.
"But I think the legendary status for him could be enhanced by winning the three grand tours. I think he should target the tour of Italy and then the Vuelta.”
With the centenary edition of the Tour rumoured to include many of its historic climbs, a defence of his 2012 title may not suit Wiggins but instead favour his Sky team mate and rival, Chris Froome.
Sky recently bolstered their Grand Tour climbing stocks for next season with the signings of Vuelta a Espana stage winner Dario Cataldo (Omega Pharma-Quickstep) and climbing domestique David Lopez (Movistar).
Wiggins came off an injury caused by a dramatic crash during the 2011 Tour to finish third behind Froome at the Vuelta a Espana (won by Juan Jose Cobo) and has raced the Giro on four occasions, his last in 2010 where he finished 40th overall, 1hr 47min 58sec behind the race winner Ivan Basso.
There he won the opening individual time trial and held the race leader’s pink jersey through the first stage.
"He (Wiggins) came third in the Vuelta (in 2011) off the back of laying on a hospital bed for six or seven weeks out after a shoulder operation. So that is doable,” said Sutton. "The Giro is a different one, it is a different kettle of fish. But if anyone can do it Brad can.”