PITTSBURGH (Reuters) - Republican presidential candidate Donald Trump will hold a campaign rally near Pittsburgh in the critical battleground state of Pennsylvania on Saturday, as suspense builds over who he will choose as his running mate for the Nov. 5 U.S. election.

Trump has said he will announce his vice presidential pick shortly before or during the Republican Party's national convention, which kicks off on Monday in Milwaukee, Wisconsin, and where he and his No. 2 will be officially nominated.

Trump mentioned Ohio Senator J.D. Vance, Florida Senator Marco Rubio, North Dakota Governor Doug Burgum and South Carolina Senator Tim Scott as possible running mates during a radio interview on the "The Clay Travis & Buck Sexton Show" on Friday.

He said there could be "four or five" people under consideration and likened the selection process to a "highly sophisticated version of 'The Apprentice,'" the TV reality show where contestants competed for a job at his company and helped turn Trump into a household name.

The decision will come at a moment of tumult for Democrats following 81-year-old President Joe Biden's faltering debate performance on June 27. A growing number of Democratic lawmakers have called for Biden to step down for a younger nominee, though Biden has insisted he plans to stay in the race.

Trump's rally on Saturday evening at the Butler Farm Show Grounds in Pennsylvania underscores the importance of the state, which Trump won in 2016 but lost to Biden in 2020.

It is again one of the handful of states likely to determine the outcome of the presidential election in November, and both men are targeting the state with visits and campaign resources.

On Sunday, Biden visited a Black church in Philadelphia and held an event with union members in Harrisburg, the state capital. Trump held a rally in Philadelphia three weeks ago, an event he billed as a chance to court Black voters.

The former president will use the rally on Saturday to talk about inflation, crime and other issues he blames on Biden, the Trump campaign said in a statement.

"I think people expect to hear who his vice president choice is going to be. I'm not sure they are going to get that," said Christopher Nicholas, a Republican consultant in Pennsylvania, about the rally. "Trump has played this close to the vest."

(Reporting by Nathan Layne in Pittsburgh; Editing by Colleen Jenkins and Rosalba O'Brien)

By Nathan Layne