The news means that Town forward James Collins will have to wait until Thursday to see if he will keep his place in the provisional squad named recently, and add to his three caps after playing twice against Georgia and Switzerland last month.
McCarthy will retain Parrott, an unused substitute in Tottenham’s Premier League draw at Everton on Sunday, when he announces his final squad, while ex-Luton loanee Connolly will also be included.
The Irish chief said: "I will announce the final squad for the friendly with New Zealand and the European Championship qualifier with Denmark on Thursday but I can confirm that Troy will be on the list.
"I spoke to Stephen Kenny at our monthly manager’s meeting on Monday and told him that Troy and Aaron Connolly will be with the senior squad next week.
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"Troy has been pushing for this step-up for some time now and I look forward to seeing him on the training ground ahead of the New Zealand game.
"I hope he pushes me to include him in that game.”
Ireland host New Zealand in a friendly on November 14 and then entertain Denmark in their crucial Euro 2020 qualifier four days later on November 18.
Goalkeepers: Darren Randolph (Middlesbrough), Mark Travers (AFC Bournemouth), Kieran O’Hara (Burton Albion, on loan from Manchester United), Keiren Westwood (Sheffield Wednesday), Caoimhin Kelleher (Liverpool).
Defenders: Matt Doherty (Wolves), Cyrus Christie (Fulham), John Egan (Sheffield United), Shane Duffy (Brighton & Hove Albion), Kevin Long (Burnley), Enda Stevens (Sheffield United), Darragh Lenihan (Blackburn Rovers), Ciaran Clark (Newcastle United), Derrick Williams (Blackburn Rovers), Ryan Manning (QPR), Nathan Collins (Stoke City)
Midfielders: Callum O’Dowda (Bristol City), Conor Hourihane (Aston Villa), Josh Cullen (Charlton Athletic, on loan from West Ham United), Glenn Whelan (Hearts), Alan Browne (Preston North End), Robbie Brady (Burnley), James McClean (Stoke City), Jeff Hendrick (Burnley), James McCarthy (Crystal Palace), Alan Judge (Ipswich Town), Jack Byrne (Shamrock Rovers)
Forwards: Aaron Connolly (Brighton & Hove Albion), David McGoldrick (Sheffield United), James Collins (Luton Town), Sean Maguire (Preston North End), Callum Robinson (Sheffield United), Aidan O’Brien (Millwall), Kieran Sadlier (Doncaster Rovers), Ronan Curtis (Portsmouth), Shane Long (Southampton), Michael Obafemi (Southampton), Troy Parrott (Tottenham Hotspur), Scott Hogan (Stoke City, on loan from Aston Villa)