The Blues boss is scheduled to meet with the club’s majority shareholder Farhad Moshiri later this week to discuss his future at the club with many expecting the 63-year-old to be sacked.
Speaking after his sides final day defeat, Allardyce said: “Confident? I can’t quite say confident after all the rumours I’m reading in the paper because generally there’s no smoke without fire.
“We’ll wait and see (what happens) when we meet up this week.”
For the fifth game in a row, Allardyce was met by vitriolic chants from the Everton fans who are ready to see the back of a man whose appointment wasn’t all that popular in the first place.
Rumours suggest that the Blues will make an approach for Shakhtar Donetsk boss Paulo Fonseca as his contract with the Ukrainian champions expires in the next couple of weeks.
Everton are also expected to return to former Watford boss Marco Silva with an offer.
Fonseca and Silva have been Moshiri’s top targets for a few weeks and the Blues were ready to pay in excess of £20 million for Silva’s services after they parted ways with former boss Ronald Koeman earlier in the year.
Should Allardyce, as is expected, depart the club then one of the Portuguese duo is expected to take over shortly after.
Another future that was up for debate was that of Wayne Rooney.
When quizzed about an update on Rooney’s situation, Allardyce said: “I don’t know other than it’s up to Wayne and his representatives and the board of directors in what they do - which I think by where it is at the moment - that everyone will know by the end of the week."
Allardyce concluded by addressing the rumours surrounding a spat between the pair being a catalyst for Rooney’s seemingly impending departure.
He stated: “Just to stop everyone talking and writing nonsense, there’s no problem between me and Wayne Rooney.
“We’ve been very professional and adult with our conversations.”