Bunn left Norwich at the end of last season, and a report in the Yorkshire Evening Post claims Leeds United wanted to sign him before he moved to Aston Villa.
The plan for Leeds was to sign an experienced goalkeeper in the summer, so as to provide cover for Marco Silvestri, whilst also to tutor Charlie Horton - who arrived at the club this summer as youth stopper.
Bunn, 30, has spent much of his career as a second-choice ‘keeper, only playing full seasons in 2006/07 and 2007/08 with Northampton Town, and 2009/10 with Sheffield United.
However, he has spent five seasons in the Premier League with Blackburn and Norwich, and is a well experienced figure in the dressing room.
Leeds wanted to bring him in this summer after he left the Canaries following their promotion to the top flight, but they were beaten to the deal by Aston Villa.
The ageing stopper agreed a two-year contract with Tim Sherwood’s men, and is set to continue his role as back-up player to Brad Guzan - having started the Premier League campaign on the substitutes bench against Bournemouth.
Following the completion of that deal, Leeds had to look elsewhere for an experienced goalkeeping option, and settled on completing the signing of former Chelsea and Middlesbrough ‘keeper Ross Turnbull.