Dasilva has made 157 competitive appearances since joining the West London club from Arsenal in the summer of 2018.
The Arsenal academy product featured in 36 Premier League matches last season to help Brentford achieve a top-half finish.
Unfortunately for Dasilva, he spent the majority of the current campaign on the sidelines after suffering hamstring and ankle issues, before he was forced to undergo knee surgery in February.
As a result of his injury troubles, the 25-year-old has been restricted to just five competitive appearances this term.
Dasilva close to extending Brentford deal
Dasilva has now entered the final two months of a four-year deal, leading to speculation over his future with the Bees.
Brentford had previously offered to help Dasilva in his injury recovery even if they decided against signing a new deal.
However, according to The Standard, the midfielder is now on the verge of agreeing a new contract with the Bees.
The report claims that the two parties have held positive talks, and there is an expectation a new deal will be announced in the coming weeks.
Mee, Onyeka to decide Brentford futures
Brentford are also in negotiations to extend Ben Mee's contract, with his current deal set to expire on June 30.
The 34-year-old made 16 Premier League appearances this season, before he suffered a season-ending ankle injury in February.
Despite his recent injury absence, the experienced defender remains a key figure in the Brentford squad, with the Bees determined to retain his experience for the foreseeable future.
While Mee could extend his stay, midfielder Frank Onyeka appears to be heading towards the exit door at the Gtech Community Stadium.
The Nigeria international has fallen down the pecking order in recent times, having failed to start any of Brentford's last seven matches.
Onyeka could look to gain regular playing time elsewhere despite having a contract until June 2027, with an option to extend by a further year.