Dan Burn's move to the Premier League edged closer at the weekend when the highly-rated defender underwent a medical at Fulham, who have made an offer for the teenager.
Everton have also made a move for Burn, who was excused from Saturday's game with Bath City so that he could travel to London.
Fulham want to ensure there will be no complications should the deal go ahead, but they face competition for the 18-year-old as several top-flight clubs are monitoring the situation.
Newcastle United, Chelsea and Manchester City are understood to have made contact with Quakers about the Northumberland-born centre-back, while Stoke City have monitored his progress.
Newcastle aborted plans to watch Burn in action on Saturday when they discovered that he would miss the match.
Every Darlington game of late has been attended by a posse of scouts but there were very few at the Arena on Saturday, aside from a disappointed representative of Norwich City.
Middlesbrough manager Tony Mowbray is another to rate Burn, who has only made 19 first-team appearances, but finances are tight at the Riverside so a bid will not be forthcoming.
Although a figure has not been publicly disclosed, Quakers hope to set a Conference record, which currently stands at £260,000.
That was set when striker George Boyd signed for Peterborough United from Stevenage in 2007.
Aside from receiving a substantial amount, Darlington also want to include a number of clauses, based on appearances plus a sell-on clause, that would ratchet up the total sum.
Speaking after Saturday's 3-1 win, Quakers manager Mark Cooper said: "There are numerous clubs interested in Dan Burn but as far as I'm aware nothing has been signed.
"The transfer window is closed so nobody can sign for anybody until the end of the season.
"There's a lot of interest in him. He's been down to Fulham, who are very keen on him, and there are other clubs that are also very keen on him.
"There are loads of clubs after him, everybody wants him, and rightly so.
"Whoever gets him will do so at the end of the season.
"For me it's important that he goes to the right club, a club that will look after him and fulfil his potential. It's not a piece of meat that we're selling."
Although Burn cannot play for another club until next season, there is a chance Quakers could agree to sell him before the completion of the campaign.
However, they would agree not to include him in any further matches, aside from the FA Trophy final, as such a measure would reduce the risk of Burn sustaining an injury.
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