Tim Iroegbunam in Everton's blue shirt
Image caption, Tim Iroegbunam has played 53 matches for Everton
The 23-year-old is poised to leave Hill Dickinson Stadium for an initial £13m, although the fee could rise by a further £9m with add-ons.
Iroegbunam, who joined Everton from Aston Villa for £9m in 2024, has been given permission to complete a medical in East Yorkshire.
It is part of a busy end to the transfer window for both clubs involved, with Hull looking to sign multiple players before Tuesday night's deadline.
Iroegbunam would become Hull's 13th signing of the summer, with talks continuing over a loan move for Chelsea midfielder Dario Essugo.
Everton, meanwhile, have agreed the £65m sale of winger Iliman Ndiaye to Manchester City.
They are close to signing Monaco striker Folarin Balogun and are in talks over moves for Manchester City winger Jack Grealish and Fulham defender Kenny Tete.
Talks over a return for Richarlison from Tottenham have stalled and his arrival on Merseyside is now not expected to happen.
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Lionel Messi holding the World Cup
Lionel Messi holding the World Cup
Sami Mokbel with a picture of Julian Alvarez
Sami Mokbel with a picture of Julian Alvarez