Simon Coveney described talks between the EU and the UK as being in a "very serious zone" and said he wa "under no illusion of the challenges" as they try to come to an agreement.
He said the next ten to 14 days is the "realistic" timeline now "to complete this".
"We're likely to get a deal but it won't be easy," Mr Coveney said.
Talks with the European Union on a post-Brexit trade deal will take place in Brussels from tomorrow.
The UK side led by Lord Frost and the EU's team under Michel Barnier have been meeting in London since the process restarted last week
In a sign that enough progress is being made to at least allow talks to continue, the teams will move to the Belgian capital to continue their discussions.
European Commission spokesman Dan Ferrie told reporters: "I can confirm that negotiations are ongoing in London right now, they will run until tomorrow and then they will take place here in Brussels, as of Thursday."
He would not be drawn on the status of the negotiations, but said both sides were "engaging intensively" to reach a deal.
On Monday, Downing Street warned "time is very short" to bridge the "significant" gaps between the UK and EU.
The current transition arrangements expire at the end of the year and a deal will need to be reached within weeks for it to be ratified by then.
The main obstacles to a deal have been rows over fishing rights, the so-called "level playing field" rules to ensure fair competition and governance arrangements for any agreement.
Mr Coveney made his comments on Tuesday during a Irish Farmers' Journal webinar.
The Fine Gael TD said the EU is working towards a "no trade deal Brexit" and there will be "no more extensions of time" when it came to the negotiations.
"There's no such thing as a no-deal Brexit any more, what we're now fighting for is a no trade deal Brexit, which from an agricultural perspective would be hugely disruptive on many, many levels," he said.
"We've got to be ready for January 1, there's going to be no more extensions of time, no more transition periods.
"Time is up at the end of the year."
The Cork South-Central TD said there would be a new trading environment on January 1 whether or not a trade deal is reached.
"If there's no trade deal it'll be on the basis of WTO standards," he said.
"If there is a trade deal that will avoid tariffs and quotas but we will still unfortunately have a lot of disruption to trade."
He warned it would take "some getting used to" for many businesses and they need to prepare for January 1.
"This is a new reality, we wish it wasn't happening but it is," he said.
"Businesses have 65 days to get their act together."
Mr Coveney added: "Can we get a deal? Yes we can. This is doable, but difficult."