The 21-year-old looks certain to leave the Bairns this summer following their relegation from the Clydesdale Bank Premier League.
Managing director George Craig said of Huddersfield's interest: "We have given them permission to talk to Scott."
He added: "A number of clubs have expressed an interest and Huddersfield have followed that up, we have had some discussions and they are ahead of the game."
Hibernian and Hamilton both had bids for Arfield rejected last summer, Southampton reportedly came close to buying him in January while Hearts have also been linked with the Scotland Under-21 international.
"Other clubs have asked to be kept informed," said Craig of the player, who has made more than 100 appearances for the Bairns since 2007.
Craig confirmed Falkirk and Huddersfield were "not too far away" from agreeing a fee, but told BBC Scotland: "It is not just about the two clubs agreeing a fee.
"It is a big decision for Scott and it has got to be the right club for him."
Source: PA
Source: PA