The Saudi prince bought a 50% stake in the Blades from McCabe in August 2013, with an option to take 100% ownership at a later date.
Prince Abdullah subsequently served notice of his intention to buy the remaining 50% of the McCabe family shares at the end of last month.
A statement on the Blades' official website reads: "His Royal Highness Prince Abdullah Bin Mosa'ad Abdulaziz Al Saud and Kevin McCabe are in discussions regarding the transfer of ownership and control of Sheffield United Football Club to the prince.
"Sheffield United Football Club is part of the Blades Leisure Limited group, a joint venture between Sheffield United Limited, controlled by the McCabe family, and companies controlled by the prince.
"Ownership of Blades Leisure Limited is governed by an Investment Agreement, dated August 30, 2013, which provides for the transfer of control of Blades to the prince.
"In response to a process commenced by Sheffield United Limited, on January 26, 2018, UTB LLC, a company controlled by the prince, served a notice exercising an option to purchase the remaining 50% of Blades Leisure from Sheffield United Limited.
"Both parties are currently in negotiation with regard to the remaining provisions in the Investment Agreement and hope to come to a final settlement in the near future.
"The Prince and Kevin McCabe want to reassure everyone connected to the club that the current negotiations and transfer of ownership will have no impact on the club's management and its staff."
The Blades were promoted as League One champions last season and are currently eighth in the Championship table.