Farke is turning to former club Borussia Monchengladbach once again, with the Leeds United boss eyeing Elvedi.
According to Bild, Farke hopes a third attempt at raiding Gladbach will finally prove successful, with the 29-year-old Swiss international his latest target.
Farke has repeatedly looked to the Bundesliga to strengthen his Leeds squad, with the current group already including Anton Stach from Hoffenheim, former Werder Bremen player Ilja Gruev and Wolfsburg's Lukas Nmecha.
He has also made a habit of trying to bring in players from his old Gladbach side specifically, having previously targeted Julian Weigl and Lukas Ullrich without success. Elvedi now finds himself the latest name on that list.
Elvedi has long expressed a desire to play in the Premier League and is reportedly using his prominent role at the World Cup as a platform to help force a move through.
Bild reports that Leeds are prepared to pay €8.5m for the defender, but that figure is unlikely to be enough to convince Gladbach to sell. The battle for Elvedi's signature appears to be only just beginning, with Leeds expected to face resistance before any deal can be completed.
Farke's familiarity with the Gladbach squad, built up over his own time managing the club, has clearly shaped his recruitment strategy at Leeds, with the manager repeatedly returning to players and profiles he knows well from his time in German football. Whether that institutional knowledge proves enough to finally land a target after two previous unsuccessful attempts remains to be seen.
Elvedi's standing at the World Cup this summer has only added to his leverage in any negotiation, with the centre-back using the tournament to demonstrate the qualities that have made him a long-standing target for Farke, even as Gladbach show little early inclination to accept a fee well below what they consider his true value.