Avaya, owned by private equity firms Silver Lake and TPG Capital, bought Nortel's enterprise division out of administration for $915m less than two months ago.
About 40 per cent of staff at Monkstown work for the Avaya part of the business.
Trades union Unite is seeking a meeting with management and has said that 140 jobs are under threat. Almost 90 workers were made redundant at the local plant in March 2009.
"Avaya has entered a consultation process following the strategic business decision to potentially close the Monkstown (Northern Ireland) office," a company spokesperson said.
Regional Industrial Organiser with Unite, Sean Smyth, claimed the prevailing situation was not looking good for Nortel workers.
"It is looking like the company are now simply turning around orders until the target date of June and after that it will be thanks, and cheerio," Mr Smyth told the Times on Tuesday.
"What is crucial now is two things. The first is the setting up of a task force involving senior politicians and the heads of government departments, Invest NI, the Department of Enterprise, Trade and Investment, employers' organisations and trade union officials to try and thrash out the promotion of sustainable jobs in Northern Ireland.
"Secondly, there must be a redundancy protection fund set up, so that what happened to the Nortel workers who were let go in March last year doesn't happen again and anyone who may fall victim to the jobs axe, benefits from an enhanced redundancy package."

Read the full story in this week's Times...