The Clarets have monitored the 24-year-old over the past year or so, with the former Rotherham United trainee twice having trials under former boss Eddie Howe, while he also played in last week’s behind-closed-doors development squad friendly with Sunderland.
Liversedge, who has Football League experience with Darlington, is believed to have impressed goalkeeping coach Billy Mercer, and he is likely to come in as an understudy to a more experienced number one, in the aftermath of the departures of Lee Grant and Brian Jensen, with Jon Stewart also likely to move on at the end of his contract this summer.
But any transfer developments between him and Burnley would be with a view to the 24-year-old starting as an understudy.
Burnley remain in the hunt for a new number one.
The Clarets have been linked with a move for Motherwell’s Republic of Ireland international keeper Darren Randolph, who is also believed to be a target for Rangers and Birmingham City. Former Charlton Athletic keeper Randolph, who is 26 on Sunday, also enjoyed a loan spell at neighbours Accrington Stanley at the start of their Conference-winning season in 2005/06.