The former Chelsea FC striker netted twice for his country in their World Cup group stage opener against Portugal on Friday night as the two sides played out a thrilling 3-3 draw.
Costa returned to Atletico Madrid last year after having been deemed surplus to requirements at Stamford Bridge by Antonio Conte.
Before his exit, he had helped the west London club to win the Premier League title in Conte’s first campaign in charge alongside Fabregas.
And his fellow Spaniard Fabregas believes that Costa could be on course to enjoy a strong World Cup with Spain this year.
Speaking to the Daily Telegraph, Fabregas said: “My old team-mate Diego Costa also showed that he can be a big player in this tournament and that he can challenge for the Golden Boot. Why not?
“The first thing I did after game was to text him because he deserves a moment like this. It’s a shame Cristiano took the headlines, but Diego did well.
“The last World Cup was a difficult time for him, especially being in Brazil in front of his family and his friends. It was a big decision to play for another country.
“But I think he feels like he owes a lot to Spain for his career – with Atletico Madrid, Rayo Vallecano, Valladolid and Celta Vigo.”
Meanwhile, Chelsea FC are believed to be on the lookout for a number of new signings this summer but the Blues are yet to make any new signings.
The west London side finished in fifth place in the Premier League table last term and won the FA Cup under Conte, whose future at Stamford Bridge continues to be a source of speculation.
Chelsea FC beat Manchester United 1-0 in the FA Cup final to win the trophy last season.
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