The two clubs, both based in Glasgow, will play each other in the competition over the weekend of March 7.
Under Scottish Cup rules, away clubs can request up to a 20 per cent allocation.
A Daily Record report suggest that Celtic have not yet submitted an official request but are expected to seek the full amount.
The report states Celtic will aim to take at least the full Broomloan Stand at Ibrox, even if they cannot guarantee more than 10,000 tickets.
Police Scotland will have a say in the number of away supporters allowed in, as safety considerations need to be taken into account for the high-stakes match.
The two clubs could come to an agreement in a ‘pre-ops meeting’ ahead of the game.
The Scottish Football Association (SFA) may intervene in the decision if an agreement cannot be reached.
This is not the only time Celtic will travel to Ibrox next month; they will also play Rangers on March 1 in the Scottish Premiership.
For this game, under a Euro-style away fan solution between the clubs, only around 2,000 Celtic supporters will be allowed to attend.
This is due to an arrangement that sees away fan numbers limited for league games between the sides.