The online petition, which has already gained over five million signatures, is asking the British Government to revoke Article 50 and to remain in the EU.
Mr Farrell commented: “Derry overwhelmingly voted to remain in the European Union.
“Over 32,000 of us realised the importance of the EU and voted accordingly on 23rd June 2016.
“A massive 78% supported continued EU membership. We had the highest remain vote in the North and the fourth highest of all constituencies.
“The petition is gaining traction, and so far, 10,000 people from Derry have signed it.
“This represents less than a third of people that voted to remain in the EU.”
Mr Farrell concluded: “Brexit is a mess and the only common sense solution is to stop it now.
“This petition is your opportunity to send a strong message to Theresa May and her cohorts that we want to stay.
The petition can be signed here: https://petition.parliament.uk/petitions/241584