The Reds are seeking a permanent successor to Markus Schopp, who left the club almost a fortnight ago following a poor start to the Championship campaign.
The Oakwell outfit, expected to opt for a overseas-based head coach for the sixth successive time, reportedly contacted Mechelen about speaking to Vrancken, but were rebuffed.
Vrancken also reportedly has a significant release clause.
Appointed in the summer of 2018, Vrancken, 42, has enjoyed success at Mechelen, leading them to a Belgian First Division B title, while also enjoying cup success and two sixth-placed finishes in the First Division B.
Mechelen are currently in fourth place in the table.
Vrancken, previously managed Belgian lower-division side Thes Sport and had brief spells at Lommel SK and as assistant at Kortrijk.
Meanwhile, assistant coach Tonda Eckert, who came to the club during the tenure of Gerhard Struber, has left Oakwell.
A number of names have been linked with the vacant position including former Newport County manager Michael Flynn, ex Norwich and Preston chief Alex Neil, who spent a spell in his playing days at Oakwell and Reading first-team coach John O'Shea.
Former target Hannes Wolf is also rumoured to be another contender alongside Alexander Blessin, head coach at KV Oostende, who are controlled by Barnsley's majority shareholder, Pacific Media Group,
Jo Laumann was in caretaker charge for the recent games against Hull and Derby.
But it is understood that the next full-time coach is again highly likely to come from abroad.