Bradley is one of two candidates still under consideration, the newspaper said. Talks are at a sensitive stage and could fall apart, it said, citing the people.
"I'm happy where I am, and I'm not planning to make any changes," the newspaper quoted Bradley as saying by phone on Tuesday night.
Motorola and HP did not immediately return calls seeking comment. Bradley could not immediately be reached.
Bradley has been with HP since 2005, and heads the company's personal systems group, which includes consumer PCs, mobile devices and TVs.
The other person on the shortlist is a telecommunications executive, the paper said. The identity of this person could not be established, it said.
Activist investor Carl Icahn has been lobbying for changes at Motorola, which has been suffering losses for more than a year.
The company, which invented the mobile phone, plans to spin off its cellphone unit next year.