Allardyce was under contract at Everton until 2019, but his time has been cut short after he grew unpopular with the fan base, leading the club to return to discussing terms with Silva.
The Portuguese remains the first choice of majority shareholder Farhad Moshiri, who initially wanted him to replace Ronald Koeman in November before Allardyce was recruited to steer the club away from the relegation zone.
Watford remain furious at Everton's initial attempts to secure Silva, which they described as an "unwarranted approach by a Premier League rival," when they dismissed him in January following a downturn in form at the Hornets. They have since issued a formal complaint to the Premier League, but it is not likely to escalate any further.
Everton offered as much as £12 million to try to secure the 40-year-old when he was at Watford, but now they can sign the unattached manager. Watford are keen to remain in the discussion, but neither Everton, nor Silva's representatives, see them as a serious threat to a possible deal.
Paulo Fonseca was also linked with the Everton job, but he is set to agree a contract renewal at Ukrainian side Shakhtar Donetsk, leaving the path clear for Silva to take charge on Merseyside.
The club's chairman Bill Kenwright is thought to prefer Bournemouth boss Eddie Howe as Allardyce’s replacement, but Moshiri holds much greater influence over Everton's big decisions.
Silva is understood to have discussed options at other clubs, with Benfica thought to be admirers of him, but Everton appears to be his preferred option for next season.
In announcing Allardyce’s departure, Everton confirmed that they would be immediately starting the process of finding the former England’s coach successor.
Director Professor Denise Barrett-Baxendale said: “On behalf of the chairman, board of directors and [owner] Mr Farhad Moshiri, I’d like to thank Sam for the job he has done at Everton over the last seven months. Sam was brought in at a challenging time last season to provide us with some stability and we are grateful to him for doing that.
“However, we have made the decision that, as part of our longer-term plan, we will be appointing a new manager this summer and will be commencing this process immediately. Again, we’d like to place on record our sincere thanks to Sam for his work with us over the last few months and wish him well for the future.”