Leeds United are said to be the first of Hugill's suitors to step up their interest.
The Daily Mirror reports on page 47 of its printed edition on Tuesday that Leeds United have 'made an £8 million move' for Preston North End striker Jordan Hugill.
It is claimed Leeds are the first of Hugill's suitors - who are also said to include Reading and Bristol City - to 'step up their interest.
According to The Sun, however, the 25-year-old is on the verge of joining Crystal Palace for an identical fee.
The Daily Mirror reports Preston want at last £10 million for Hugill, who has hit double figures for the second season running.
And any such Leeds move would come as some surprise, given what Angus Kinnear, United's managing director, told BBC West Yorkshire Sport last Wednesday.
Asked why the Whites could not go in with an offer of £8-or-9-million plus £20,000-a-week for Hugill, for example, Kinnear said: "Well I think it's not that we couldn't, because I think we have the potential to do that. But it's about making sure we get value for the player.
"I think that, when you look into the market place at the minute and we look at players and we assess whether they can make the type of impact that we need across the rest of the season, and then look at the financials around the deal - it's about assessing whether you can get value.
"And a lot of the names that have been suggested in the press I don't think have the potential to deliver - or are significantly better than what we have currently.
"And I also think they would be a departure from our model of being able to operate sustainably from a financial perspective."
Middlesbrough-born Hugill arrived late into league football, joining Port Vale from Whitby Town four-and-a-half-years ago.
And it was Simon Grayson, the former Leeds boss, who took him to Preston 12 months on.
Would Hugill be a good signing for Leeds?