The 34-year-old is currently without a team following his release from Queens Park Rangers earlier this month.
However, despite having a large part of his career blighted by injuries, the midfielder is said to have no intention of retiring from the game.
As a result, his appearance at Ipswich's Playford Road training base this week has started rumours that he could sign on with his boyhood club until the end of the season.
Dyer began his career with Ipswich in 1996, before going on to join Newcastle United in 1999. Then, while on the books of West Ham United, he had a brief loan spell back at Portman Road in 2011.