Mr Coveney made the comments as efforts intensify to find a way through the Brexit impasse with the April 12 deadline looming.
She stressed that ultimately "the solution has to be found by Great Britain itself" and expressed hope that Prime Minister Theresa May "will be successful".
On Tuesday Mr Varadkar held talks with French President Emmanuel Macron in Paris.
The leaders will participate in a roundtable discussion in Dublin with people from Northern Ireland and the border area ahead of their meeting, the Irish government said.
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But he again reiterated his opposition to creating a hard border between Ireland and Northern Ireland, for fear that it could jeopardise peace in the British province.
"These are people for whom the border is a very real issue - people from communities along the border, from business, and with direct personal experience of conflict before the Good Friday Agreement".
"My trip to Ireland is to the country which..."
Speaking in the Irish parliament, Mr Varadkar said: "I don't know if Mr Corbyn will rise to the occasion, whether he will show leadership and be able to come up with a compromised plan with Prime Minister May".
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After a broadly successful meeting with French President Emmanuel Macron on Tuesday, Mr Varadkar will be hoping Ms Merkel will send a message to European Union colleagues by playing down the possibility of checks at the Irish Border in a no-deal scenario.
He said "reasonable questions" are being asked about the protection of the single market and the customs union.
European Union chief negotiator Michel Barnier said Tuesday that Britain is getting closer and closer to having its exit from the EU go forward with no deal in place on the terms of its withdrawal.
But differences are emerging between the two sides as the possibility of a "no deal" Brexit looms, which would lead to the creation of a border between the United Kingdom territory of Northern Ireland and Ireland.
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Lyft posted a loss of $911 million in 2018 versus $688 million in 2017, despite revenue doubling in 2018 to $2.16 billion. A smartphone app for Lyft drivers is seen during a photo opportunity in San Francisco, California February 3, 2016.
"It is important to hear their voices as we work together to deal with the challenges that Brexit presents".