If the two clubs cannot agree on a fee for the 19-year-old, the case will be brought before a tribunal.
Buckle said: "I hope that any tribunal will acknowledge the amount of work that has gone into Carayol's development over the last two years."
Carayol agreed a move to the Imps last month, bringing his two-year spell at Plainmoor to an end.
The midfielder, whose contract with the Gulls is set to finish at the end of the month, was offered another deal by Buckle at the end of last season, but turned it down in favour of Lincoln's offer.
The BBC understands Lincoln are still hopeful of agreeing a compensation deal for Carayol, but recognise if that does not happen the case could go to a tribunal.
Compensation for players who are under the age of 24 is awarded in recognition of the money the club has spent on development of the player.
Source: BBC Sport
Source: BBC Sport