The Toffees may be sitting in 13th, but they’re only five points clear of the bottom three and have won just four times in the Premier League all season.
In fact, they have won just twice in 13 games in all competitions, which simply isn’t good enough.
It’s form that would worry any manager, let alone someone coming into a team that spent big in the summer.
Despite Everton’s big money buys, they appear to have gone backwards and Allardyce will surely splash the cash to help them stay up, as there is no doubt the Toffees are in a relegation battle.
But who should he target? We’ve identified six players who the new Everton boss may look at.
Allardyce is a fan of Luke Shaw – he called him up to his one and only England squad when Three Lions manager.
Shaw is a huge prospect, even if he does appear to be on his way out of Manchester United.
He needs game time ahead of the World Cup, and a move to Everton could be what he needs to revitalise his career.
If it doesn’t work out, there is always Baines to fall back on. But if it does, they could have a left-back for the next ten years given Shaw is just 22.
When struggling sides are searching for players to keep them up, they rarely target a player who suffered relegation last season and is struggling in second-tier.
However, Allardyce got the best out of Koné at Sunderland and a reunion could benefit both manager and player.
Everton’s defence is weak, despite the arrival of Michael Keane in the summer, and the new Toffees boss will surely strengthen that part of his team.
The Blues did attempt to sign the Ivory Coast centre-back in the summer of 2016, but Sunderland stood firm.
Speaking at the time, it was clear he wanted to move, saying: “Everton, they are not a small club. There were other clubs interested too. But it was not concrete like Everton. It was a very good opportunity for me. A golden opportunity. They are playing for the top positions. They could be in Europe.”
While of course they are not at the table, there is still no doubt that the 28-year-old would jump at a move to Goodison Park.
Another England international struggling for game time ahead of the World Cup next summer is Theo Walcott.
The Arsenal winger has made just three appearances in the Premier League this season, all off the bench.
His World Cup dreams look like fading away once again and he definitely needs a move in January that can see him set the top flight alight.
The Toffees bought several No.10s in the summer, meaning the likes of Gylfi Sigurdsson have been playing out wide, a role that Walcott would undoubtedly perform in far better the Icelander.
Allardyce is also clearly a admirer of the 28-year-old – he called him up for his only England squad back in 2016, when the Arsenal man wasn’t in favour internationally.
The Bournemouth striker only arrived on the South Coast in the summer and has scored just one Premier League goal this season.
He’s not a guaranteed starter though, having come off the bench in five of his 11 league appearances for the Cherries.
Aged 35, he is approaching the twilight of his career, but he is a proven Premier League striker, which Everton need following the departure of Romelu Lukaku in the summer.
He’s worked previously with Allardyce at Sunderland and when in charge at Crystal Palace, Big Sam spoke up a potential deal: “If we are safe and Jermain Defoe is available, and he wants to come to Crystal Palace, I would be interested.”
Of course, that didn’t end up happening, with the striker going to Bournemouth and Allardyce leaving Palace.
But it does prove that despite his advancing years, Allardyce would be keen on having Defoe in his side.
While Defoe would be a short-term solution up front, Cedric Bakambu would be a long-term answer.
Deceptively quick, strong and with a real eye for goal, the Villarreal forward is one of the stars so far of La Liga.
He has nine goals in 12 league games so far this season and the Congolese striker is ready made for the Premier League. It’s unlikely he would need time to adapt.
Villarreal were reportedly asking for around £20million in the summer, but now, expect the club to want his buyout clause met if they let him go in January given his importance to the team.
That’s at around £35million, a figure Everton could easily afford.
Given Allardyce has complained about a lack of chances for British managers, perhaps he’d want to give a chance to British players too.
While the Gunners probably wouldn’t want to sell him permanently, they may be tempted by a loan move for their 22-year-old defender, who has started just three times in the Premier League this season.
If he struck up a decent partnership with Michael Keane, it may even be music to England’s ears as they look for an up-and-coming defensive duo.