Ba joined Chelsea from the Magpies for £7million just seven months ago.
The Mirror reports that the two clubs are in talks over the highly-rated 28-year-old striker.
Ba scored 29 goals in 54 games during his 18-month spell at Newcastle.
Ba is currently not a regular under new Chelsea manager Jose Mourinho.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.