Costa was roped in by the Blues for 32 million pound ($32.4 million) in 2014, and was understood to be close to a return to former allegiance Atletico Madrid after a spluttering 2015-16 season.
Chelsea were given a stiff examination by Stoke City at Stamford Bridge on Saturday before extending their lead at the top of the Premier League to six points.
Diego Costa struck as Chelsea won 1-0 at Crystal Palace on Saturday, a club record-equalling 11th straight victory that sent them nine points clear at the Premier League summit.
Diego Costa was on target again as Chelsea overcame a defensive West Bromwich Albion 1-0 to return to the top of the Premier League
Diego Costa starred as Premier League leaders Chelsea roared back to win 3-1 on Saturday in an ill-tempered game at Manchester City, who had Sergio Aguero and Fernandinho dismissed.
Chelsea replaced Liverpool at the top of the Premier League with a comfortable 1-0 win at Middlesbrough thanks to a first-half Diego Costa strike on Sunday.
Diego Costa's sublime strike sealed Chelsea's 2-0 success against Southampton on Sunday as the Blues chalked up a fourth successive Premier League victory.
Jose Mourinho will always have a place in the hearts of Chelsea's faithful but his former charges are hoping to make him suffer when he returns to Stamford Bridge as manager of Manchester United on Sunday.
Willian and Diego Costa scored twice in six second-half minutes as Chelsea won 2-0 at Hull City to claim a first win in four Premier League games.
Costa scored twice, including an 81st-minute equaliser, as Antonio Conte maintained his unbeaten start to life as Chelsea manager in a 2-2 draw at Swansea City on Sunday.
Diego Costa scored a goal in each half to lead Spain to an 8-0 rout of Lichtenstein in Group G of European qualifying for the 2018 World Cup on Monday.
Costa thrust himself back into the headlines with an 89th-minute winner as Chelsea edged West Ham United 2-1 in Antonio Conte's first Premier League game as manager on Monday.
The 27-year-old, who joined the London club from Atletico in 2014, did not feature in Chelsea's 3-2 defeat by Real Madrid in a pre-season friendly on Saturday due to a back injury.
Atletico Madrid president Enrique Cerezo has ruled out Chelsea forward Diego Costa's possible return to the Vicente Calderon stadium this summer despite reports suggesting otherwise.
Conte indicated that striker Diego Costa will stay at the club, despite a series of reports in the Spanish media linking him with a return to Atletico Madrid.
The nationalised Brazilian missed Chelsea's last two games of the season due to a persistent hamstring injury and has struggled at international level with just one goal in 10 games since declaring to play for Spain in 2013.
Chelsea striker Diego Costa must serve an extra one-match ban after being sent off in last month's FA Cup tie at Everton, the Football Association said on Friday.
The English Football Association has charged Chelsea striker Diego Costa with improper conduct after being sent off in Saturday's FA Cup loss at Everton.
Costa leapt up from the pitch and thrust his head into Barry's before moving his mouth towards his neck and motioning as if to bite the Everton midfielder.
Chelsea manager Guus Hiddink says Diego Costa broke his nose in training but still expects the striker to be available for the English Premier League game against Newcastle on Saturday.
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