British Prime Minister David Cameron wants a looser arrangement with the EU. He will set out his policy in a major speech this week amid intense speculation of a referendum on the extent of his country's EU membership.
Mr Gilmore backed up Taoiseach Enda Kenny's view that it would be a negative development, describing it as "rocking the boat".
Speaking on Sky News, he said the focus of the EU needed to be on job creation.
"At this critical time, we need to concentrate on the things that Europe needs to do."
Mr Gilmore also emphasised the close working relationship between Ireland and Britain on EU affairs, since both countries joined the then EEC. He said it was important in a modern economy for this work to continue.
"We are dependant on each other," he said.
Mr Kenny warned last week the EU's "floodgates" would be opened if the Lisbon Treaty was revisited to suit an individual country.
"We would see it as being disastrous were a country like Britain to leave the union. Clearly, the British government will form its own view," he said.
During his visit to Dublin, European Council President Herman van Rompuy also said Britain would be better off staying in the EU: "Britain is a highly appreciated, highly valued and very important member of the EU. I believe it is in British interests to stay."
The prospect of Britain leaving the EU has also set off alarm bells in Washington.
The Obama administration issued a direct challenge to Mr Cameron last week, also warning of the dangers of holding a referendum on Britain's EU membership.