It comes after UK Foreign Secretary Liz Truss held her first meeting with European Commission vice-president Maros Sefcovic since taking over Brexit negotiations following the resignation of Lord Frost.
However, the party has argued that its pressure over the Protocol is what has led to the current negotiating talks with the EU.
Mr Coveney said he does not want to see the the Northern Ireland Assembly election in May become dominated by the “polarising” issue.
Speaking on Friday, Mr Coveney said the meeting marked a “reset” in the relationship between the EU and UK teams, which is now “in a better place than we’ve seen for a while”.
He said: “From my conversations with both sides, I think that process will be a very serious one.
“I think in people’s minds, really, we would like to have, if possible, these issues resolved by the end of February, so that the elections in Northern Ireland can move ahead without being dominated by the Protocol issues, right the way to polling day.
“Elections in the North are often polarising enough affairs without having the added complexity and tension around the Protocol and its implementation.
“So I think everybody is conscious of their responsibility in terms of trying to bring some stability and certainty to Northern Ireland in the context of Brexit, and the Northern Ireland Protocol. ”
Ms Truss said there is a “deal to be done” following her meeting with Mr Sefcovic.
However she refused to rule out the possibility the UK could invoke Article 16 – suspending part of the arrangements in the Protocol – if they could not agree a way forward.
Mr Coveney insisted the Protocol is here to stay, and that he did not expect the UK to remove the threat of Article 16 until a deal is agreed.
He told RTE Radio One: “The Protocol is there. It’s part of an international treaty, it’s part of international law.
“And so the focus really on the EU side is how do we implement this Protocol in a way that is pragmatic and flexible, and takes on board the genuine concerns that have been raised in Northern Ireland?
“I think if both sides work on that basis, there is a landing zone that can be agreed over the next six or eight weeks.
“As an Irish government perspective, we will be working to try to assist that process.”
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