The controversial Spain international has so far refused to return to West London having spent the entire summer in his homeland of Brazil.
In a series of media interviews, the 28-year-old slammed manager Antonio Conte for dropping him from his plans and accused the club of treating him like a criminal.
According to Marca, the Premier League champions have so far been refusing to sanction Costa's desired return to Atletico as they want him to come back to the UK to train with the reserves.
However, the Spanish publication states that the Blues have now softened their stance and are prepared to discuss a deal with the La Liga outfit, who are banned from registering new players until January.
It is believed that the fee could be around €60m (£54m), which would break Atletico's transfer record.