Manchester United had previously discussed a £60m fee for the Spain worldwide, but they were eventually put off with Los Blancos demanding more than £70m for their graduate.
With Romelu Lukaku set to join the Red Devils and Tiemoue Bakayoko's deal hindered, Antonio Conte's eager to land the Colombian to reinforce his attacking choices.
Catalan newspaper Mundo Deportivo reports that Morata is upset with how Madrid handled the transfer process, making it sound like they dragged their feet for a few extra dollars.
Chelsea value the Spain star at £60m, although Atleti do not want to pay more than £22m for the 28-year-old striker who has only two years left on his contract.
The offer would be less than the £80m Real Madrid had quoted United for Morata.
Now Chelsea may be tempted to turn their attentions to Morata, with the less than reliable Sky sources in Italy reporting Stamford Bridge officials have already made contact with Real Madrid as they plot a move.
Both Blancos stars have always been linked with a Santiago Bernabeu exit this summer, with teammate Luka Modric having today warned the pair of the risks of departing 'best club in the world' Real Madrid.
The reigning European champions want to free up funds to make a world-record bid for Kylian Mbappe this summer.
Luis Muriel to Sevilla: Luis Muriel has completed his move to Sevilla from Sampdoria after passing a medical at the LaLiga club, signing a five-year deal at the Ramon Sanchez Pizjuan.
Conte was the mastermind behind his move from Real Madrid to Juventus in 2014.
That's a pretty big spread, and given the weakened position that Stamford Bridge is negotiating from, it could take a while to see an agreement reached, if one even is.
On Tuesday, it was reported that Chelsea were also keeping tabs on Borussia Dortmund striker Aubameyang who is available to purchase in the current transfer window.