The Express report that Swansea are demanding £30 million for the prolific 26-year-old forward, but the reigning Premier League champions want to pay closer to £25 million.
If talks break down then Chelsea are ready to pounce. It’s understood that scouts at Stamford Bridge have run the rule over the former Vitesse striker, on the instruction of Jose Mourinho, several times this season.
No Premier League player scored more goals over the course of 2014 than Bony, who Swansea paid £12 million for in July 2013.
Manchester City remain hopeful of securing a deal for the Ivorian within the coming days, but Swansea’s reluctance to sell for a lower price leaves Chelsea in with a chance of signing the player.
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Mourinho wants another striker
The Blues successfully offloaded Fernando Torres to AC Milan last month and Mourinho clearly feels his side require another striker heading into the second half of the 2014-15 campaign.
The west London outfit attempted to bolster their attacking options with the signing of Croatia international Andrej Kramarić, but the 23-year-old opted to join Premier League strugglers Leicester City instead, in the hope of nailing down a first-team place at the King Power Stadium.
While Kramarić would have been a useful back-up option, Bony is only likely to agree to join Chelsea if they can offer him regular first-team football.
Bony deal could upset Chelsea strikers
Mourinho already has one world-class striker in his ranks: Diego Costa, who Chelsea risk upsetting by signing another forward seeking regular first-team football.
Bony’s arrival would also push both Loic Remy and club legend Didier Drogba further down the pecking order - although it’s understood that the latter is in the early stages of considering his retirement from the sport.
Pellegrini refuses to confirm Bony news
Meanwhile, Manchester City manager Manuel Pellegrini has admitted that he plans on signing another striker this month, but refused to name Bony as his number one transfer target.
"I don't talk about rumours,” the Chilean said in his press conference on Friday. “We are going to replace Alvaro Negredo because it was the decision that we've taken that we're going to sell him.
"We said we'd see in December if we need another striker. We need another striker so we are going to find which is the best player to play here."