Promoter Eddie Hearn wants to build on Brook's impressive points victory over Matthew Hatton in front of 10,000 fans at the venue earlier this month.
The welterweight is close to earning a world-title fight and Hearn is hoping to bring a big-name opponent to the 25-year-old's hometown this summer.
"It was a fantastic night in Sheffield for Kell and for British boxing, and I had no hesitation in putting him on in the Arena again," said Hearn.
"Kell delivered in a big way against Matthew and proved he is worth the hype. Now we will deliver another big night for him against a top name that we will announce soon."