According to Alberto R. Barbero of Marca, Costa's desire to play for his former club again "was the main reason why Chelsea were unable to negotiate with Everton."
The Toffees are said to have made the aforementioned offer, as well as a "bonus." AC Milan were reportedly interested in Costa too, but he wanted to head back to Atletico for a second spell.
The transfer from Chelsea to the Madrid side has yet to be finalised, though as noted by the latter's Twitter account, the deal is close to being done:
As we can see courtesy of La Liga's Twitter account, Costa was at Atletico's new Wanda Metropolitano stadium on Saturday for the team's clash with Sevilla:
According to the Guardian, the 28-year-old's transfer will be worth around £57 million to Chelsea, who bought Costa from Atletico for £32 million in 2014.
In the three seasons he spent at Stamford Bridge, the Spain international came to be adored by the Blues faithful. His brutish forward play left so many defences unsettled, while the goals he scored helped the team to some big results.
Chelsea won two Premier League titles during the time Costa was at the club, as he led the line expertly.
Here's how prolific he was:
As BBC Sport noted, despite being a key part of the title-winning side last season, manager Antonio Conte marginalised the forward in pre-season, and he has not featured for the Blues in 2017-18.
While a move to Atletico didn't go through before the summer deadline, it appears as though the Spanish outfit weren't the striker's only admirers. Everton were on the hunt for a forward, having lost Romelu Lukaku to Manchester United in the summer, and they were seemingly desperate for another physical presence up top.
As Squawka Football noted ahead of the team's win against Sunderland in the Carabao Cup on Wednesday, the Toffees have been having big issues in front of goal:
Costa, a proven winner and a thoroughbred goalscorer in the Premier League, would have been a big help for Ronald Koeman's side. And while the aforementioned sums may seem excessive for a 28-year-old, signing a player of such calibre would have represented a real statement from the Toffees.
Eventually, the three parties involved in this deal look like they've got what they want. Chelsea will receive a big fee for a footballer they don't want around, Atletico will have a world-class striker to add to their squad in January and Costa is back at his spiritual home, where he will hope to give the Rojiblancos the best years of his career.