The Magpies have banned the Mail on Sunday and sister paper the Daily Mail from all games and press conferences after the Sunday paper published comments made by Triesman which had been secretly recorded by a friend of his.
As a result Triesman resigned as chairman of the FA and England's bid for the 2018 World Cup.
Newcastle had been considering a request from the Daily Mail for a previous ban to be revoked when the story was published last week.
The club said in a statement: The Daily Mail have recently made approaches through the Association of Editors for the ban to be reviewed.
Newcastle United Football Club were considering that request when The Mail on Sunday decided to publish its disgraceful story about Lord Triesman.
That story was not in the best interest of English football and has had enormous adverse repercussions already with regard to the 2018 World Cup bid.
Newcastle United Football Club supports the stance taken by Gary Lineker who has ceased to provide a column for the newspaper and has been outspoken in his criticism.
The Daily Mail and The Mail on Sunday, will be unwelcome at Newcastle United for the foreseeable future.
The club has also written to the Premier League and all other Premier League chairmen, asking for their support in Newcastle's stance against these publications.
Newcastle, meanwhile, could be priced out of a move for unsettled Manchester City centre-half Nedum Onuoha.
Onuoha is keen to leave the City of Manchester Stadium this summer, having made just ten first-team appearances last season.
The former England Under- 21 international is one of a number of players interesting Chris Hughton.
With Danny Simpson facing a race to be fit for mid-August as he recovers from an ankle injury, Hughton would like to sign a player capable of playing at both right-back and centre-half.
Onuoha fits the bill, but City officials will demand around £6m before allowing the 23-year-old to leave.
Hughton will be unable to offer that figure, as it is likely to represent a significant proportion of his entire summer budget.
Meanwhile, Newcastle winger Jonas Gutierrez is an injury doubt ahead of Argentina's World Cup opener with Nigeria on June 12.
Gutierrez, missed training yesterday with a muscular problem.