Dave Whelan, chairman of the Lancashire side, appointed former Bolton boss Coyle in the summer, and was asked if he could see the FAI contacting him about the former Dundee United striker replacing Giovanni Trappatoni as manager of the Republic of Ireland national side.
Trapattoni endured a torrid time at the 2012 European Championships, with Ireland scoring just one goal and letting in nine and their recent 2-1 home defeat to Sweden in a World Cup qualifier has left them with a mountain to climb if they are to reach the finals in Brazil in 2014.
Recent results have led to some people questioning the 74-year-old’s abilities, and Coyle was one name mentioned as a possible replacement.
Whelan said: “You never know. One thing [Owen] said to me when I gave him the job was ‘If Celtic ever come in I want the job at Celtic’.
“That’s one thing I respect.”
Coyle has taken charge of six Wigan matches since replacing Roberto Martinez, and has won two, drawn two and lost two.