The rapper faces competition from clothing brands Izod and Southpole, who also seek to have the 26-year-old arena named after their flagship brands.
According to the Bergen County Record, The New Jersey Sports and Exposition Authority (NJSEA), which is handling bids for the naming rights, said a new name for the famed arena could emerge as early as October 4th.
"We're looking forward to presentations by bidders next week, and then we'll get into the process of evaluation," he said. "I'm optimistic that we'll be able to overachieve the current financial deal that we [had] with Continental."
Continental had been paying over $600,000 a year for the naming rights to the arena. NJSEA officials expect to double that figure with the new naming-rights holder.
The new owner will hold the rights to the arena's name for two years, when the Nets move move to Brooklyn in 2009.
Representatives for Jay-Z were not available for comment as of press time.