Both Leeds and RB Leipzig want to snap up the highly-rated 18-year-old defender and bids for his services have gone in to Dinamo Zagreb.
Leeds are claimed to have offered €22m plus a 20 per cent sell-on clause, while RB Leipzig have not gone above €15m.
The Premier League side appear in pole position for Gvardiol, but according to Croatian outlet Sportske Novosti, the teenager prefers a move to Germany.
Gvardiol wants to stay at Dinamo Zagreb, but he is of the view that if he does leave, RB Leipzig would be the better move.
While the centre-back considers the Premier League his dream league, he thinks that given where he is in his career, moving to a club just promoted from the Championship could be a step too far.
RB Leipzig have a record of developing players, something Gvardiol has noted, and he is keen to move to a club with a clear plan to improve him.
All eyes are now on RB Leipzig to see whether they can get close to the amount put on the table by Leeds for Gvardiol.