Whoever gets the job could have a new striker on the books as Tigers vice-chairman Ehab Allam is believed to be hoping to land Hungary’s Nermanja Nikolic.
The 28-year-old would cost £3m from Legia Warsaw, who need him first for their champions League qualifiers against Dundalk.
Former Watford and West Ham manager Zola is a late contender to be appointed the new head coach of Hull if the club’s latest offer, which is said to quadruple his current wages to £1.5m per year, fails to prise Coleman from Wales.
The Welsh FA are already believed to have made contingency plans to bring in Ryan Giggs, who quit Manchester United when his role under new Old Trafford manager Jose Mourinho was diminished.
Legend Giggs, who made 64 appearances for his country, would be a popular replacement ahead of Wales’ World Cup qualifiers.
Hull’s fellow promoted club Middlesbrough, who retain an interest in Tigers central defender Harry Maguire, have been linked with Greek midfield man Andreas Samaris, who would cost around £16m from Benfica.
Leeds United could move in for Lyon midfield player Oliver Kemen, who has made two appearances for the Ligue 1 outfit, if they fail to complete a permanent deal for Sunderland star Liam Bridcutt.
Sheffield Wednesday are said to be ready to hand centre-back Tom Lees a £25,000-a-week deal in an attempt to ward off interest from Burnley, Derby and Fulham.
The Clarets would make an offer if Michael Keane leaves for Leicester City.