Leipzig's preferred solution is to extend their loan arrangement with Gruda, the 21-year-old German under-21 international currently on loan from Brighton.
Negotiations are ongoing over a second loan, potentially with a purchase option or obligation attached. If that deal collapses, Elliott becomes a genuine alternative.
The 23-year-old is returning to Liverpool in the summer after a loan spell at Aston Villa that Unai Emery publicly described as embarrassing for all involved. Elliott made just nine appearances at Villa Park, accumulating around 284 minutes and triggering widespread concern given that a threshold of ten appearances would have activated a 40 million euro mandatory purchase clause.
Emery was candid about the situation.
"The situation with Harvey Elliott is embarrassing for all parties. I'm sorry for the boy. My apology to Harvey is in my thoughts every day."
Elliott returns to Anfield with one year remaining on his contract, and a sale in the summer is considered likely at a fee in the region of 15 to 20 million euros.
His connection to Leipzig's head of global football Jürgen Klopp adds an interesting dimension. Elliott made 119 appearances under the German during his time at Liverpool, and the pair are said to have maintained a close relationship. Whether Klopp's proximity to the Leipzig structure could influence the club's pursuit remains to be seen.