The Hornets filed the complaint earlier this year after deeming Everton's approach for Silva last November as illegal, with Sky Sports reporting that, to date, all efforts to reach an amicable solution have failed.
The news comes after Silva once again emerged as Everton's leading candidate to replace the now confirmed outgoing boss Sam Allardyce - six months on from the first clash between the two clubs.
Watford have claimed that illegal negotiations were held between Silva and Everton after the Merseysiders sacked Ronald Koeman in October, a meeting which formed part of the grounds for which Silva was dismissed for in January.
The Premier League subsequently instigated a mediation meeting for the two clubs last month but the issue failed to be resolved, and with the dispute having dragged on for four months the league could be forced to find a conclusion to the issue themselves.
If such action were to be taken by the league then the panel could impose a range of sanctions which could include fines through to possible points deduction for Everton, should accusations of poaching Silva are proven.
The report claims that the most likely scenario would be a suitable compensation figure reached for Everton to pay to their Premier League rivals.
Watford remain angered by Everton's repeated attempts to lure Silva to Goodison Park over a two-month period which unsettled the Portuguese boss and led to a dramatic dip in form on field - after one win was notched in 11 matches.
The Hornets' statement at the time of Silva's departure read: "The club is convinced the appointment of Silva was the right one and had it not been for the unwarranted approach by a Premier League rival for his services we would have continued to prosper under his leadership."
Having then appointed Allardyce in place of Koeman, Watford felt they received assurances that the Toffees would not pursue their former boss as a summer target, and if Silva is to be named as the next manager then Watford are reportedly prepared to explore their options.
A lengthy legal dispute could therefore delay Everton's hopes of a quick managerial appointment this summer.