Middlesbrough, Norwich City and the Reds are all keen on the 26-year-old midfielder according to Sunday newspaper reports.
Former Southend man Bailey has netted 25 goals in 87 league games for Charlton since his 2008 move but their failure to gain promotion from League One could see his exit this summer.
Middlesbrough meanwhile have been linked with a £1.5m move for Peterborough's George Boyd, a Forest loanee towards the end of last season.