The Manchester Evening News says Jones is not gaining any interest.
The 29-year-old was once a highly rated teenager and arrived from Blackburn Rovers in 2010 to much fanfare. But injuries have plagued his career over the past two years.
Jones still has two years remaining on his contract and might need to run it down before he can depart for free.
Burnley were widely reported to be keen earlier in the summer but that interest has seemingly gone cold.