Text messages between Zappone and Minister Coveney also revealed she had spoken with Finance Minister Paschal Donohoe about the position.
Former Minister Katherine Zappone was told about her appointment as UN Special Envoy four months ahead of the job being discussed by Cabinet.
In WhatsApp messages released by the Department of Foreign Affairs on Monday Zappone said that she had also spoken with Finance Minister Paschal Donohoe about the position.
On March 4, Zappone texted Coveney saying: “Hi Simon, thank you so, so much for offering me this incredible opportunity. It will be such a privilege and I will be so proud to serve Ireland again. I think the time is really ripe for change too.
“Could you let me know time period appointment is for, and what are next steps," she added.
"As you know I am working with UNFPA till mid or end of June. Thank you again so much Simon - especially when you have so much on your plate. I spoke with paschal too yesterday. Warmest, Katherine.”
Donohoe told Newstalk's On The Record programme on Monday that Zappone approached him late last year "regarding a future in the UN", adding that he suggested she contact Coveney for advice which he mentioned to him in early 2021.
"I had no further engagement with Minister Coveney on the matter," he said.
Coveney previously told the Oireachtas that he had only communicated Zappone's availability to his Department, however, the UN office didn't start pulling together a brief for it until mid-June, three months after the former Minister had already thanked Coveney for the role.
It comes as Tánaiste
Leo Varadkar shared screenshots of messages between himself and Minister for Foreign Affairs Simon Coveney as well as former minister Katherine Zappone last week.
He later issued an
apology after it was revealed that texts between him and former Minister Katherine Zappone were not disclosed when requested by journalists under Freedom of Information (FOI) law.
The Department of the Tánaiste had responded to an FOI request on 23 August stating that there were
no messages exchanged with Zappone in relation to the controversial Merrion Hotel event in July.
Speaking to reporters in Dublin last week, Coveney said that the reason he had deleted the texts from his own phone was due to hacking concerns.
"I change my phone every year. I've been hacked and I'm the Minister for Foreign Affairs and Defence - so I think it's prudent that I clear my phone fairly regularly," he said.
Asked about the messages with the Tánaiste, Coveney said they exchanged messages "a number of days" before Varadkar was due to meet Zappone in Dublin, and he asked if there was "anything you want to brief me on".
Coveney said that he had texted back that he was working with Zappone and his department about a "... potential role as a special envoy, but I will be bringing the details to Government in the coming weeks - and that was it.
It comes as on Tuesday evening, the Minister for Foreign Affairs and Defence noted at a meeting that he routinely deletes text messages for storage space reasons.
Coveney sought to clarify the matter on Wednesday, insisting that any related texts that were later deleted were part of a regular habit of clearing messages.
Coveney also stated that he changes his phone once a year for security reasons.
Last month it was reported that an event at Merrion hotel on 30 July was attended by Tánaiste Leo Varadkar and around 50 other people, just days before the appointment of Zappone to the UN envoy role.
The event generated a significant degree of controversy since, not least as it was made without the knowledge of Taoiseach Micheál Martin.
Zappone has since confirmed that she would not accept the appointment to the role.
