(Reuters) - Former Bear Stearns chief executive Alan Schwartz may not join JPMorgan Chase as non-executive vice chairman, the New York Post said on Monday, citing a source familiar with the matter.

Schwartz, 57, had been inclined to accept JPMorgan's offer, but is not pleased that more than half of Bear's employees are now jobless, the newspaper said, citing sources.

Another matter weighing on Schwartz's status could be whether JPMorgan has cooled on bringing him in, given that the bank already employs well-known dealmaker in Jimmy Lee, the newspaper said.

JPMorgan did not immediately return calls seeking comment.

In a U.S. Securities and Exchange Commission filing in April, JPMorgan had said that senior Bear officials may eventually accept employment with the bank. Among these were Schwartz, chief financial officer Sam Molinaro, controller Jeffrey Farber and general counsel Michael Solender.

On Saturday, JPMorgan said it had completed its $1.4 billion takeover of Bear Stearns, capping the demise of a Wall Street firm that was felled by the mortgage crisis.