Silva, 36, signed for Chelsea as a free agent last summer after leaving French giants Paris Saint-Germain following their European Cup final defeat to Bayern Munich.
The veteran centre-back was brought in by Frank Lampard to bring experience to the defence, and impressed with a number of top performances.
Silva also became a key player for Lampard’s successor, Thomas Tuchel, with Chelsea’s strong back line - expertly marshalled by the Brazilian - a fundamental reason for their eventual Champions League success.
Silva cut a dejected figure as he was forced off injured during the first half of Saturday night’s clash against Manchester City, but the defender did not have to endure successive Champions League Final defeats as Kai Havertz led Chelsea to glory.
Though Silva has suffered a few frustrating muscle injuries as age caught up with him, the defender is set to stay at Stamford Bridge for another season as Tuchel looks to build on the club’s glorious night in Porto.
Silva signed an initial one-year deal with Chelsea with the option of a further year, and Standard Sport understands the option is being taken up to tie him down until summer 2022.
While Tuchel has the likes of Kurt Zouma, Andreas Christensen, Antonio Rudiger and Cesar Azpilicueta all impressing along with Silva in a back three, Chelsea could also look to add another defender this summer.