German outlet BILD report that questions remain over the 29-year-old defender's future at the club. Elvedi's situation needs to be resolved in the coming weeks, with Gladbach already planning around him and looking to sign players who could complement him in defence.
The plan is to have his position doubly covered, though that depends on Elvedi agreeing to extend his current contract, which runs until 2027.
A decision is required this summer, with time running short for both player and club.
Should Elvedi show no interest in extending his stay, sporting director Rouven Schroder is expected to push for his sale rather than risk losing him for nothing. Allowing him to leave on a free transfer next summer would represent a significant loss for Borussia Monchengladbach, given his standing in the squad.
That scenario would work firmly in Leeds United's favour, with the Premier League club having been linked with a move for Elvedi since last month.
The Swiss international is understood to be keen on a switch to the Premier League, and a renewal at Gladbach is considered unlikely if that opportunity materialises.
Leeds will be monitoring the situation closely as Gladbach's self-imposed deadline approaches, with Elvedi's decision likely to shape the direction of the transfer saga in the coming weeks.
Gladbach's willingness to move quickly on reinforcements underlines the importance the club places on covering the centre-back position, regardless of which way Elvedi's decision ultimately goes. For Leeds, the prospect of negotiating with a selling club rather than facing resistance to any approach would represent a considerably smoother path to completing a deal this summer.
The defender's contract situation means Gladbach face a difficult balancing act, needing to plan for his possible departure while also leaving the door open to a renewal should his stance change.
With the Swiss international's preference for a Premier League move already known, much now depends on how quickly Gladbach are willing to act if no agreement over an extension is reached.