Unused substitute Callum Murray was in the Buckie squad that drew 0-0 with Formartine United on Saturday but the club deny any wrongdoing.
The Moray club could secure the title with a win at home to bottom club Strathspey Thistle this weekend.
The league's eventual winner will have the chance to join the SPFL next term.
Victors of the Highland and Lowland Leagues will meet in a play-off to decide who should face the Scottish League Two bottom club in the League Two play-off final.
A meeting of the Highland League's management committee will be held on Thursday.
Murray had been on loan to rivals Deveronvale but was recalled by Buckie as cover for injured players and sat on the bench throughout Saturday's goalless draw.
Whether he was eligible to be involved or not will come down to the interpretation of the Highland League's rule 8.9.6, which governs the registration of players.
Any breach is subject to a fine of up to £500 and a mandatory three-point deduction for each game affected.
SHFL secretary Rod Houston told the BBC that Thursday's meeting had become necessary "after a storm on social media".
Buckie and Cove Rangers are two points behind leaders Brora Rangers but Brora have played all of their games.
Cove face Lossiemouth on Saturday in the final game of the season and Buckie have a superior goal difference going into their meeting with Strathspey.
In season 1992-1993, Elgin City won the Highland League but were later stripped of the title after having been found to have fielded ineligible players.
Scottish Highland Football League title challengers Buckie Thistle could face a damaging points deduction amid claims they listed an ineligible player.