The Blues are willing to spend big this winter with Everton expected to sell Barkley, as the midfielder is out of contract in the summer and therefore able to walk away for free, per John Cross at the Mirror.
Barkley is yet to feature for the Toffees this season due to a hamstring injury, although the supporters have not forgotten about him, according to the Liverpool Echo's Adam Jones:
Caretaker manager David Unsworth has said "he would love" the midfielder to stay at Goodison Park, per Neil Jones at the Liverpool Echo.
Chelsea saw technical director Michael Emenalo leave on Monday, amid growing tensions with manager Antonio Conte over the club's transfer activity last summer, per Sami Mokbel for the Daily Mail.
Barkley has denied he underwent a medical with Chelsea over the summer and said he would decide his future in January, via Twitter:
With his contract expiring, Everton are unlikely to reject a large bid for Barkley in January, making him an attainable target for Chelsea.
The Blues are also interested in strengthening their attack and want a quality back-up to Alvaro Morata, with Benteke a player that Conte likes, per Cross.
The Italian has not been convinced by Michy Batshuayi, even though he has seven goals in all competitions for the Blues this season, per BBC Sport.
Benteke, meanwhile, is yet to open his account in the Premier League this season and has been wasteful in front of goal, as shown by WhoScored.com:
While Morata has proven a strong signing, with eight goals already for Chelsea, the departure of Diego Costa does leave the Blues short in attack, particularly if Conte does not trust Batshuayi.
Benteke would certainly provide power and presence up front, but his is not a signing that will excite fans, particularly after he failed to impress at Liverpool.
The striker joined the club in 2015 in a big-money move but lasted a little over a year before being sold to Crystal Palace in August 2016.