Chelsea are said to have made an opening offer of £33million for Arturo Vidal.
But a report in Colombia claims that Blues will have to stump up closer to £53m if they are to snare Vidal, 30, from Bayern Munich.
Antonio Conte knows the Chile midfielder from his time in charge of Juventus, where the duo won three Scudettos together.
Boss Conte has made it clear that he wants more cash to revamp his side.
The Italian has hinted that a lack of spending meant the a Blues title tilt “never started”.
And on Boxing Day he spoke of his admiration for a Vidal – a player Conte says he’d “go to war with”.
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Yet he spent £177m on new signings over the summer in preparation for his side’s Prem title defence.
Two of those additions were Tiemoue Bakayoko and Danny Drinkwater, who accounted for a combined £75m of that outlay.
But it is claimed that Conte still wants to add further strength to his midfield in the form of the all-action Vidal.
The 97-cap Chile legend has just 18 months left on the four-year deal he signed to join the German champions in 2015.
Vidal, who has also won the Copa America and German title twice, will not be going to Russia 2018 after Chile missed out on qualification in the final round of South American matches.