The Reds have launched a £24.6m bid for Shakhtar Donetsk's attacking midfielder as boss Jurgen Klopp looks to bolster his attacking options.
Chelsea thought they were in pole position.
But Anfield chief executive Ian Ayre flew to Florida to hold face-to-face meetings with Shakhtar, who are in America for winter training.
Ayre is believed to have flown back to Merseyside last night but discussions are continuing.