Blues boss Antonio Conte is looking to tie up as many as four deals in the final few days of the transfer window.
Arsenal’s Alex Oxlade-Chamberlain has already agreed to move to Stamford Bridge and Chelsea want a number of other Premier League players too.
The Telegraph report that Conte and co are looking to land Oxlade-Chamberlain, Barkley, Leicester’s Danny Drinkwater and Swansea striker Fernando Llorente.
And it is said Chelsea have already tabled an offer for England midfielder Barkley.
Everton have been demanding upwards of £50m for the 23-year-old this summer.
But the Toffees are now aware they won’t get such an amount and are currently in negotiations with Chelsea over the fee.
Ronald Koeman’s side hope Tottenham, who have tracked Barkley for months, will launch a bid of their own following Chelsea’s move and push his price back up.
Barkley wants to leave Goodison Park and move to London and neither Chelsea or Tottenham are put off by his current hamstring injury.
The young star will be out for at least another three months but the London duo want to get a deal done during this transfer window.
Chelsea have now leapfrogged Spurs in the race to secure his signature but any potential transfer still has a way to go yet.
