The Whites want the teenage Italy international this summer and boss Jesse Marsch has admitted the player is rated at Elland Road.
Zurich are prepared to sell Gnonto, but want in the region of €8m after reducing their asking price from €10m.
Leeds held a conference call with Zurich on Saturday to discuss a deal for Gnonto, according to Italian broadcaster Sportitalia, but no agreement was reached.
The Premier League side are offering €5m, but are around €3m plus bonus payments short of presenting a deal Zurich would find acceptable.
The situation is being monitored by Italian Serie A side Monza.
Monza are ready to move into the race if Gnonto has still not left Zurich by the closing days of the transfer window.
A move to Serie A could appeal to the Italy international if no deal can be done with Leeds.
Whites managing director Angus Kinnear admitted on Saturday that his side are finding it challenging to sign new players at present.
