That is according to former Toffees boss Sam Allardyce, who says Liverpool star Andy Robertson evaded his old club’s grasp too.
Maguire joined Leicester from Hull last June in a deal worth £17m and has since established himself as an England international.
The 25-year-old played a key role as the Three Lions reached the World Cup semi-finals this summer and that attracted interest from Manchester United.
Maguire’s fortunes contrast markedly to those of Michael Keane, who has been capped by England and left Burnley for Everton 12 months ago.
Keane’s stock has fallen since his switch to Goodison Park and he faces being shunted down the pecking order by Yerry Mina and potentially Kurt Zouma’s arrivals on Merseyside.
Allardyce has now claimed Everton could have snapped up Maguire around the same time Ronald Koeman bought Keane from Burnley.
And he’s revealed Robertson, who’s gone on to thrive at rivals Liverpool, could have been part of a double-deal with Hull too.
“[Everton] were [close to getting Maguire]… I was told by Steve Walsh, who was the director of football when I got there that that was a very big opportunity for them to take Maguire and, [Walsh] said, Robertson,” Allardyce told talkSPORT.
“Both from Hull City, what a pair they would have been.
“That’s what I’m talking about recruitment, Alan [Brazil], you can ill-afford any slip-ups.”
TalkSPORT host Alan Brazil offered his own take on the revelation Allardyce made on Thursday morning.
“Maguire and Robertson, oh dear,” said Brazil.
“Evertonians, I hope I’ve not spoilt your breakfast.”
Meanwhile, Everton are yet to announce the capture of Mina from Barcelona.
However, Barcelona say Mina has joined Everton on a permanent deal worth £27.2m (€30.25m), plus £1.35m (€1.5m) in bonuses.
Barcelona have inserted a buy-back clause into the agreement for the centre-back, who shone like Maguire at this summer’s World Cup.
Barcelona have also confirmed Andre Gomes’ loan to Everton, with Marco Silva’s side stumping up £2m (€2.25m) for the deal and agreeing to pay his wages for the duration of the 2018/19 campaign.
Mina and Gomes join Bernard, Richarlison and Lucas Digne in putting pen to paper at Everton, while Chelsea’s Zouma could seal a loan switch with a deal sheet lodged with the Premier League.
Richarlison (Watford) Undisclosed
Lucas Digne (Barcelona) Undisclosed
Joao Virginia (Arsenal) Undisclosed
Bernard (Shakhtar Donetsk) Undisclosed
Yerry Mina (Barcelona) £27.2m
Andre Gomes (Barcelona) loan
Joel Robles (Real Betis) Free
Jose Baxter (released)
David Henen (released)
Ramiro Funes Mori (Villarreal) Undisclosed
Wayne Rooney (D.C. United) Undisclosed
Luke Garbutt (Oxford United) Loan
Henry Onyekuru (Galatasaray) Loan
Shani Tarashaj (Grasshopper Club Zurich) Loan
Davy Klaassen (Werder Bremen) Undisclosed
Ashley Williams (Stoke City) Loan
Antonee Robinson (Wigan) Loan
Kevin Mirallas (Fiorentina) Loan
Callum Connolly (Wigan Athletic) Loan
Read more here: Daily Express :: Sport Feedhappy wheels
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