Fernando Torres will join Milan permanently on January 5 ahead of his expected return to Atletico Madrid.
Liverpool boss Brendan Rodgers has insisted Mario Balotelli will not be going out on loan in the January transfer window.
The 24-year-old was one of four players listed by the London Road outfit earlier this month for a breach of discipline.
Gabriel Zakuani was taken off the list by the Posh, but Nathaniel Mendez-Laing, Tyrone Barnett and now Sinclair have all moved on after being told they could go.
Sky Sports revealed last week that Barnsley failed with a bid for both Barnett and Sinclair, but now they have returned to finalise his capture.