As a part of the agreement, the U.S. government will have a veto over any equipment purchases by Sprint from new vendors, if the two companies were to merge, the newspaper said.
U.S. Senator Charles Schumer had expressed strong concerns on Friday about SoftBank's plan to buy a majority stake in Sprint, warning it could expose the United States to Chinese cyber attacks.
If Sprint gains control of Clearwire Corp and SoftBank in turn gains control of Sprint, the Japanese company has agreed to remove equipment made by China's Huawei Technologies Co from Sprint's networks, the paper reported.
Last week, Clearwire approved Sprint's sweetened buyout offer after Sprint raised its bid to $3.40 per share, from $2.97 per share, for the 50 percent it does not already own.
SoftBank bid $20.1 billion last October for a 70 percent stake in Sprint. Dish Network Corp countered with its own $25.5 billion offer in April and quickly launched an offensive to undermine SoftBank's standing with regulators and the public.
Sprint plans to form a four-person national security committee, including a security director who will sit on Sprint's board, the Journal reported.
A final agreement is likely to be reached in the coming days, the paper reported.
(Reporting by Supantha Mukherjee in Bangalore; Editing by Anthony Kurian)