The Toffees were left short in attack after selling Beto to Fiorentina on deadline day, only for a proposed move for Monaco striker Folarin Balogun to collapse in the final hours when the player himself refused to sign despite both clubs agreeing terms.
Everton also had a late loan approach for Manchester United's Joshua Zirkzee turned down, leaving David Moyes with Thierno Barry as his only recognised out-and-out striker heading into the new season.
Brennan Johnson arrived from Crystal Palace in a swap deal that saw Dwight McNeil move the other way, and while the former Tottenham forward could be asked to fill in up front, it is far from an ideal solution for Moyes. Everton have ended the window with just 18 outfield players in the senior squad, according to The Sun, underlining the scale of their recruitment problems.
Vardy, 39, has been a free agent since leaving Serie A side Cremonese, where his contract expired at the end of last season after the club were relegated to Serie B. He turns 40 in January but has continued to attract interest from a host of clubs since becoming available, including Championship side Wrexham, whose approach he turned down, as well as reported offers from Sheffield Wednesday, West Ham United and Brazilian giants São Paulo.
The former Leicester City striker remains one of the most prolific goalscorers of the Premier League era, having netted 145 top-flight goals across a 13-year spell at the King Power Stadium that included the 2015/16 title win and the 2019/20 Golden Boot.
Because Vardy is currently a free agent, Everton would be able to register him outside the usual transfer deadline, giving Moyes a route to bolster his attack even with the market officially closed, reports The Sun.
Vardy spent one season in Italy after leaving Leicester, scoring seven goals in 29 Serie A appearances for Cremonese, but was unable to prevent the club's relegation back to Serie B. He has previously ruled out an emotional return to Sheffield Wednesday, the club that released him as a teenager before his rise through non-league football with Stocksbridge Park Steels, Halifax Town and Fleetwood Town on his way to Leicester.
Everton's chaotic window has left Moyes facing mounting scrutiny after failing to add proven attacking reinforcements at any stage, with the club's supporters increasingly frustrated by the club's recruitment strategy heading into a season that will demand far greater squad depth than Everton currently possess.