The Sun says the only stumbling block to the move is concerns about the player's fitness.
Ba failed a medical at Stoke two years ago and has a chronic problem with his right knee. But he has not missed a single training session at Newcastle.
Ba moved to Tyneside on a free after West Ham were relegated from the Premier League in 2011.
He was paid a basic £20,000 a week plus £25,000 for every game he played because of worries about his fitness.
Chelsea are not believed to be after a similar deal for a striker who had a £7.5m release clause in his contract and will pocket £2.5m of that as a loyalty bonus.