The Daily Star says Hughton was among the frontrunners when the Baggies were last looking for a boss after sacking Roberto Di Matteo 15 months ago.
And he did spurn several chances to declare himself out of the running for a switch across the Midlands.
Hughton said: “I can’t affect any speculation or deal with things that aren’t fact.
“The only thing that is fact is that we have two massive matches that are taking up 100 per cent of my focus.”
Albion chairman Jeremy Peace is set to move swiftly to get his man, with former Hawthorns favourite Michael Appleton, 36, a likely second choice.