The 22-year-old has been attracting interest from across throughout the last year as his deal with the Royal Blues ended in July, but Meyer has been unable to find a new club so far, unlike former teammate and fellow free agent Leon Goretzka who has joined Bayern Munich.
It had been suggested that Arsenal would look to sign Meyer early in the summer transfer window. However, the club's chief negotiators are unwilling to sign the Germany international midfielder unless he lowers his wage demands.
The Gunners' decision to delay talks with Meyer has caught the attention of Liverpool, who have previously been linked with a move for the Olympic Silver Medalist, and the Reds are now considering an official offer, according to the Sunday Express (via the Daily Star).
It has been rumoured that Meyer's arrival at Anfield could put speculation over the club launching another attempt to sign Lyon's Nabil Fekir to bed. However, many expect that the Frenchman will still join Liverpool ahead of the new season.
Meyer has spent nine years rising through the ranks in the academy of Schalke 04, the bitter rivals of Klopp's former side Borussia Dortmund.
Naturally an attacking midfielder with 146 Bundesliga appearances to his name, Meyer was used in a deeper role under manager Domenico Tedesco as the Royal Blues finished second in the league table.