The Blues, with the likes of Diego Costa, Loic Remy and Radamel Falcao, find themselves in a strange position of not being able to fire in front of goal and see the 22-year-old as the answer to their goalscoring woes.
And he could be available for as little as £20 million given his value is only due to decrease, with it unlikely the striker will sign a new deal at the Hawthorns.
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Berahino was the subject of a dramatic summer transfer saga which saw Tottenham vying for his signature late in the window, though a deal was ultimately scuppered by the Baggies.
As a result, the striker publically vented his frustration and insisted he would never represent West Brom again, targeting chairman Jeremy Peace.
However, after the dust settled and a talk with manager Tony Pulis, Berahino eventually came to terms with his role at West Brom and a move to White Hart Lane seemed a distant memory.
And yet now, with January on the horizon, it looks like a bit of deja vu for the Baggies with Mourinho interested in bringing Berahino to west London.
Peace's frail relationship with Tottenham chairman Daniel Levy ultimately stopped Berahino's move dead in its tracks in September, but the current chase for West Brom's prized asset could mean the 59-year-old has an unwinnable fight on his hands to retain a player with ambitions to play at a higher standard.
The England starlet is joint top goalscorer at West Brom with new boy Salomon Rondon, also on three goals, and the few sparks he has shown this season amongst a less creative Baggies side could show Mourinho that the striker may well be worth the £20 million in January.
Chelsea fans: is Berahino the answer to your woes in front of goal? Or does Mourinho need to aim higher? Let us know your thoughts!