The same paper report that Leicester do not want to sell one of their star players and consider the central midfielder to be worth much more than Chelsea are now offering.
The report says the Foxes have put a £40m price-tag on the midfielder - the same fee the Blues received for Matic.
The champions have been linked with a £30m move for the 27-year-old in the hope of reuniting him with former Leicester midfielder N'Golo Kante and recreate the midfield combination that played such a major role in Leicester's Premier League triumph two seasons ago.
"I'm always looking for the positives, we came to the Emirates and the players executed the game plan".
However, he did partner exceptionally well with Kante at the King Power Stadium in 2015/16.
However, the Blues boss knows he needs to further strengthen if Chelsea are going to compete on all fronts this season and the Evening Standard claims director Marina Granovskaia has stepped-up the clubs pursuit of new players with Conte wanting up to four more new arrivals before the end of the month.More news: Two survive plane crash unreported for hours
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"We were quite good previous year on corners and I believe with a bit of work, we can get that out of the system".
Riyad Mahrez, who has stated his desire to leave, is another Leicester player attracting interest, with Roma unsuccessful in a £32m bid and Arsene Wenger a fan.
Regarding their interest, it seems that is likely to die down now that they're on the verge of re-signing Marten de Roon, also a defensive midfielder, from Middlesbrough.
The France worldwide came off the bench to head home in the 85th minute as the Gunners kicked off the Premier League season with a thrilling 4-3 win.
According to the French website, Atalanta also made a loan offer with a view to buy, but met the same resistance from Leicester the Ligue 1 sides have had to deal with all summer.
"I can only speak on how I've found him coming back, he has been focussed and driven", said the Leicester manager.