President Barack Obama is scheduled to attend a Corzine campaign rally at the PNC Arts Center in Holmdel, NJ on Thursday, and media outlets have been speculating that Corzine will announce his pick by then.
Corzine campaign spokesman Patrick McKenna told The AP candidate background checks are still ongoing and no decision has been made.
While Trump declined comment when asked if he'd spoken to Pinkett about the lieutenant governor's post, he said the 38-year-old's victorious run during The Apprentice's Fall 2005 fourth season does provide him some insight into his politics.
"He was dealing with lots of smart people from Harvard, Yale, Princeton, and he emerged as the leader of that group and a popular leader," Trump told The AP.
"He didn't do it with the stick; he did it a lot softer than that."
New Jersey State Senators Barbara Buono and Loretta Weinberg are also reportedly being considered as running mates by Corzine.
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