Sinclair, 27, has reportedly agreed terms and will complete the deal, thought to be worth around £4m, once he travels north to complete his medical.
The former England youth international had his most productive spell working under Rodgers at Swansea City. He netted 27 goals in Swansea’s promotion season of 2010-11 and scored eight times in the Premier League the following season before an ill-fated £8m move to Manchester City. He’s since spent time on loan at West Brom and Aston Villa before joining the Midlands club at the beginning of last season.
Celtic have left a spot open in their Champions League squad to face Hapoel Be’er Sheva. They have until Monday to sign and register Sinclair so he’s available for the play-off round clash.