With Stuart Hogg on an extended injury lay-off, New Zealand-born Baker would give Warriors some much needed cover at full-back.
The Sunday Times claims Warriors are weighing up a move for the 28-year-old.
Baker spent last season at Zebre but is thought to be keen on a move with the recent turmoil at the Italian club clouding the squad's contractual situation.
Baker played under Dave Rennie at Manawatu and went on to play Super Rugby with Highlanders. He has represented Maori All Blacks and New Zealand 7s.