Blues boss Jose Mourinho is desperate to land a world class striker to spearhead his team, and is ready to spend big once the next transfer window is open in order to do so.
The likes of Edinson Cavani and Diego Costa were rumoured to be his top targets, but now it has emerged that Suarez is on the radar.
The Uruguayan international has been in the form of his life in recent months, smashing in an incredible 23 Premier League goals in just 19 appearances.
Despite his form and the fact he penned a new contract shortly before Christmas, there is speculation suggesting that he could leave at the end of the season if Liverpool fail to finish in the top four.
Suarez angled at a move away from Anfield last year in search of Champions League football, and Chelsea are keen to take advantage if they can in six months’ time.
Even though the Reds are against doing business with a domestic rival, Mourinho is ready to test their resolve with a £55m offer.
However, he is likely to face competition from Real Madrid and Arsenal – both of whom were keen on him last summer.