However, despite relegation from the SPL, the Westfield club are keen to hold on to their players.
"Just because Falkirk have been relegated does not mean we will be selling any player on the cheap," a club source told BBC Scotland.
"For any player sold during the summer we will be looking for the full market value of the player."
Arfield was a target for Hamilton and Hibernian last summer, but Falkirk rejected bids of £100,000 and £300,000 respectively for the Scotland Under-21 international.
Manager Steven Pressley hopes to retain the core of his side as they attempt to return to the top flight of Scottish football at the first time of asking.
And BBC Scotland has learned that its unlikely that the club would listen to offers for winger Ryan Flynn or defender Brian McLean.
Source: BBC Sport
Source: BBC Sport