Bookies' favourite Paul Heckingbottom is in contention to become the new manager of Bradford City, just days after he was sacked by Leeds United.
Former Liverpool trickster Hammill worked with incoming Rangers manager Steven Gerrard at Anfield.
The Barnsley winger could join a former teammate in Australia.
The Barnsley manager is 2/1 to replace Simon Grayson at Sunderland - could the following Aston Villa and Reds stars follow him north if appointed?
Hammill was sent off in Barnsley's last encounter with Sheffield Wednesday in December.
Winnall left Barnsley to sign for Sheffield Wednesday in January.
The former Wolves man reacted badly to being substituted in the Tykes defeat.
The 28-year-old scored in a recent 4-0 win at Molineux.
Johnson, who swapped Oakwell for Ashton Gate in February, is said to be courting players from his old club and Preston North End.
Barnsley's Adam Hammill is wanted by Championship sides Reading and Bristol City, a report claims.
HITC Sport understands that a man linked with Preston North End of late is ready to leave the John Smith's Stadium.