According to The Express, the Brazilian centre-back, who signed a one-year contract upon his arrival in August, will commit to another season with the Blues.
Silva was one of Frank Lampard’s major additions to the squad, bringing considerable experience and leadership skills to a team that has relied on youth more recently.
Chelsea were the Premier League’s biggest spenders by a considerable margin last summer, recruiting Hakim Ziyech, Timo Werner, Ben Chilwell and Kai Havertz for huge fees.
In contrast, Silva joined on a free transfer after his trophy-laden eight-year spell at PSG came to an end.
Silva was a key factor in establishing PSG’s domestic dominance as they lifted seven Ligue Un titles and multiple cups during his stay at the club.
The Champions League was always their main aim and they came closest to success last season, losing 1-0 in the final to Bayern Munich.
Despite his age, the 36-year-old keeps himself in peak physical condition and is confident of carrying on into his forties.
Although he has missed a few games with a thigh problem recently, Silva has still made 21 appearances in all competitions, many of them as captain.
With his standing in the game, Silva has already become a respected figure in the Chelsea dressing room and someone whose mentality inspires others.
He will keep playing an important role under Thomas Tuchel, particularly if the German manager continues to field three centre-backs.
He has plenty of options to choose from, with Kurt Zouma, Cesar Azpilicueta, Andreas Christensen, Antonio Rudiger and Silva all comfortable in a back three.
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