Rice is widely expected to leave West Ham this summer and David Moyes has more or less admitted to the possibility of losing him in the coming months.
Several Premier League sides such as Manchester United and Liverpool are interested in him, but Arsenal have the lead in the race to sign the England midfielder.
Arsenal are keen to get a deal over the line soon and were in talks with West Ham over signing Rice.
But it has been claimed that West Ham have put a hold on the negotiations over the midfielder’s departure.
The Hammers want to wait until a potential Europa Conference League final before considering selling the player.
Arsenal want to do their business early in the summer but are now facing a delay if they want to sign the West Ham captain.
West Ham will travel to AZ Alkmaar this week for the second leg of their Europa Conference League semi-final, which they are leading 2-1.
The club and Rice want to focus on winning the European competition at the moment over a transfer move at the moment.
Rice will also feature for England at the end of the season, which could further delay a transfer.