The mistake makes it unlikely the letter writer will be charged with jury tampering, though the Journal said a final decision has not been made.
The letter prompted Judge Michael Obus to declare a mistrial in the six-month long trial.
Other jurors have said Jordan had been siding with the defense, the Journal said.
The letter expressed anger at Jordan for appearing to want to acquit two senior executives of Tyco charged with using the company as a piggy bank.
Former Tyco Chairman Dennis Kozlowski and ex-finance chief Mark Swartz, in one of the biggest corporate corruption cases in U.S. history, were accused of looting Tyco of $600 million.