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Sunderland face a battle to hang on to Lamine Kone with Chelsea now challenging Everton for the Ivorian, according to sources.

But while reports claim the Black Cats have been rebuffed in an attempt to include Phil Jagielka in any transfer of Kone to Goodison, they are understood to be keeping close tabs on Anderlecht’s Kara Mbodji and Blackburn Rovers’ Shane Duffy should they need to swoop for a centre-back.

Everton have stepped up their pursuit of a central defender, or two, following John Stones’ £47.5 million move to Manchester City.

They have agreed a £12 million fee with Swansea City for Ashley Williams.

Yet that is not thought to have curtailed their search for defensive reinforcements, with Kone next on their shopping list.

A bid of £15.3 million is said to have been rejected by Sunderland for a player only signed - from Lorient, for £6 million - in January.

Kone is under contract at the Stadium of Light until 2020.

But sources suggest Everton have increased their offer to £18 million, with a five-year deal on the table for the 27-year-old. Advanced talks are ongoing, they add.

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A reported attempt by David Moyes to secure the services of Jagielka - who signed for the Toffees under the Scot from Sheffield United in 2007 - in part-exchange for Kone appears to have failed.

But Sunderland may yet benefit if Chelsea firm up their interest in the defender, and thus drive up his price.

Napoli’s Kalidou Koulibaly is said to be Antonio Conte’s first choice as he seeks a new centre-back, but Kone is being considered as a back-up option.

In terms of contingency plans of their own, Sunderland have been linked with Anderlecht’s Senegal international Mbodji, a player Moyes had scouted as long ago as 2010, when the 26-year-old was at Tromso.

While the Black Cats have also been credited with an interest in Blackburn’s Republic of Ireland star Duffy.

The 24-year-old is out of contract next summer, so could be secured for a modest sum, but Sunderland face competition from West Bromwich Albion, Brighton & Hove Albion and Celtic for his signature.