The 19-year-old, who joined the Gunners academy as an eight-year-old, featured in EFL Cup wins over Norwich City, Doncaster Rovers and West Ham United last season.
Dasilva was also an unused substitute in last season's Europa League win over Red Star Belgrade.
According to the Birmingham Mail, the Blues may be willing to exploit a loophole to snap up the versatile player on loan despite being under a transfer embargo.
The report states that the EFL will permit the signing of a player if the club's current squad consists of fewer than 24 senior players and if the salary of the incoming player is less than £600,000 a year.
Meanwhile, if the club in question have 24 players exactly, they can sell a player and replace him with a player who is on 75% of the wages of the outgoing player and, again, is below the £600,000 mark.
Birmingham currently have fewer than 24 senior established players, and so are able to bring another player in under these particular guidelines, and Desilva has reportedly been earmarked as the player in question.
Dasilva was part of the England team that won the Under-19 European title last year.