Invista is seeking 48 voluntary redundancies at its plant at Clooney Road, Maydown, but said it has no current plans for compulsory job cuts.
SDLP Foyle MP Mark Durkan, Sinn Féin MLA Maeve McLaughlin and DUP MLA Gary Middleton have been meeting management.
Mr Middelton said he was told there are no plans for compulsory redundancies.
"I will remain in contact with the firm over the coming weeks and months and have told them of my willingness to assist them in any way so they can continue operating here in Londonderry and providing very valuable employment in the area," he said.
Mr Durkan said the Invista decision was disappointing.
"On previous occasions I have worked with Invista's local management to lobby on regulatory proposals which they were afraid would threaten the Maydown site's capacity to compete for future in-company investments," he said.
"I will be seeking clarification on how this disappointing news fits with the local management's previous active anticipation on risks to future investment and employment prospects at Maydown."
Ms McLaughlin said information was needed on workers' options and redundancy terms.
"First and foremost, it's a difficult time for employees," Ms McLaughlin told BBC Radio Foyle.
"There's no easy time to get news like that, but I think particularly this time of year, coming up to Christmas when people have families, there's extra consideration."
She said she wanted the firm to clarify its redundancy terms after complaints from the workers' union and added she would be asking about retraining opportunities.
In a statement, the firm's site manager Kevin Kelly, said: "Given the increasingly global competitive market, Invista has offered employees at its Maydown site the opportunity to apply for severance under a voluntary severance offer to improve the site's productivity.
"This offer aims to help create a sustainable staffing profile, appropriate for Invista Maydown's operations plans and needs for the future.
"We intend to assess the level of interest of the voluntary offer before considering our next step. There are no plans for a compulsory redundancy exercise at this time," Mr Kelly added.
Management of a US textile firm that plans to cut almost 50 jobs at its Londonderry site have met politicians to discuss staffing.