Mr Coveney said he believed an agreement would be made, despite the two sides being “miles apart” on fisheries.
Mr Coveney said: “My assessment of this is a deal can be done here.
“I believe a deal will be done here but there’s a lot of difficult work to do and I think it is going to take weeks rather than days to finalise this.
🗣 The message from Minister @simoncoveney is clear, act now, get informed, and take steps to get your business #Brexit ready.
Changes are coming, go to https://t.co/3MkhlNGZK1 for more on the resources and supports available. https://t.co/4HYYtJeqkn— Brexit Ready Ireland (@BrexitReadyIRL) October 15, 2020
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“I hope that by the start of November that we will be in the space of a deal in sight.”
But Mr Coveney warned that if it took until November to reach agreement, time would be “really running out”.
The Fine Gael TD made the comments during a parliamentary committee meeting on the implementation of the Good Friday Agreement in Dublin on Thursday.
Mr Coveney described fisheries as a core issue that could prevent a trade agreement between the two sides.
“The EU is not going to sell out its fishing industry to get a trade deal on Brexit. Both sides need to understand that,” he said.
“Fishing won’t be sacrificed to get a deal here.”
I believe a deal will be done here but there's a lot of difficult work to do and I think it is going to take weeks rather than days to finalise this
Mr Coveney told politicians that if an agreement was not reached in time, the aftermath of a failed negotiation and the blame game that would follow would create “enormous uncertainty” for everyone.
He said it was going to be “difficult enough to manage” the new reality from January 1 alongside trying to deal with Covid-19, even if a deal is done and an agreement is in place.
He told the committee that it was “vital” that the protocol in the Withdrawal Agreement was implemented “in full and in good faith”.
He said the EU and Ireland had outlined their “profound concern” to the UK Government over its Internal Market Bill.
“The UK must move away from the path it has chosen in the Bill and work to rebuild trust on implementing the WA in full and in good faith,” he said.
“The absence of that makes other agreements very difficult.”
He said the Irish Government was “particularly concerned” by suggestions from the UK Government that its unilateral approach was designed to protect the Good Friday Agreement.
“The protocol itself is specifically designed to protect the agreement and the gains of the peace process including avoiding a hard border,” he said, adding “we spent literally years trying to design it in order to do that”.
He added it was important that the Good Friday Agreement was not “misrepresented” in Westminster.
“The twisting of what the Good Friday Agreement actually is is a big, big issue that all of us need to be aware of and need to respond to,” he said.
“Just like we need to make sure that here in Dublin or anywhere else for that matter, we don’t exaggerate or misrepresent the Good Friday Agreement.
“I think we’ve to make sure that’s not happening elsewhere either, particularly in Westminster.”