"I prepared myself for what was being said by the press a couple of days before". Everton finished the season in eighth place on Sunday. Speculation has grown that the former Sevilla manager is the number one choice to replace David Moyes at West Ham.
Marco Silva and Paulo Fonseca are among the early candidates in line to replace Allardyce.
The London Stadium club are in the market for a marquee appointment and have been linked with former Manchester City boss Manuel Pellegrini.
Moyes succeeded Slaven Bilic in November, when West Ham were in the relegation zone, and guided the team to safety. The recruitment last summer was overwhelmingly poor and this resulted in a extremely hard season, with the style and tactics used under Allardyce proving very hard to watch. Instead, he is leaving yet another Premier League club. He also had a disappointing stint in Spain with Real Sociedad.More news: Distant galaxy hints at universe's earliest stars
It is not clear why exactly Silva is not interested in considering the West Ham job, but perhaps it should concern the Hammers fans ever so slightly given that he is not a marquee name in comparison with some of the others on the shortlist.
While the former England boss successfully delivered Premier League safety and a solid eighth place finish, supporters had grown exhausted of the club's inconsistency and poor style of football.
The club officially stated on Wednesday: "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".
Speaking to Talksport on Thursday, the 63-year-old said: "Something as delicate as that, whether you're parting company or going to have a meeting on it, is something you want to be confidential and not out in the open before it happens".More news: Angry Alabaster Trump Supporting Lawyer Under Fire For Threatening Spanish-Speaking Workers
"So these guys get fired right, they're gone, see you later, take care".
Allardyce, whose previous clubs include Bolton, Newcastle, Blackburn and Sunderland, landed his dream job with England in 2016 but that turned sour after only one match, with Allardyce stepping down following a newspaper sting.
Silva remains the favourite to take the helm at Goodison Park, having left Watford in December.
Rooney, 32, needs to know if he figures in the club's plans after months of frustration under Allardyce.More news: World Cup squad France says no to Payet