McCarthy replaced Martin O'Neill in charge of Ireland in November 2018 for his second spell, having managed the country between 1996 and 2002.
Ireland clinched a 3-1 friendly win over Bulgaria in Dublin on Tuesday which ensured McCarthy is unbeaten in eight matches, with the country also top of Group D in Euro 2020 qualifying.
The Football Association of Ireland's plan is for McCarthy, 60, to hand over the reins to Under-21 coach Stephen Kenny when his tenure comes to an end after Euro 2020.
And when asked if there was a chance his contract would be extended if Ireland were to qualify for the tournament, McCarthy responded with an emphatic "no" and then refused to be drawn much further on the subject.
"You know the situation. I've just said no," McCarthy said.
"Hopefully we qualify for the Euros and it [the succession plan] will be seen as a really good decision."
McCarthy gave five players their international debuts against Bulgaria.
Goalkeeper Mark Travers and midfielder Josh Cullen started, while Jack Byrne, striker James Collins and shot-stopper Kieran O'Hara all came on during the second half.
Ireland secured victory thanks to first international goals from Alan Browne, Kevin Long and Collins, which left McCarthy satisfied.
"Ultimately the result pleased me the most," McCarthy said. "Josh Cullen deserved man of the match – he was excellent.
"Alan Browne was also excellent. I loved James Collins' performance when he came on. Jack Byrne lit the place up with his forward passing and created two goals."
McCarthy also revealed he will ask left-back Stephen Ward to come out of international retirement for their crunch Euro 2020 qualifier against Georgia next month.
Ward, 34, retired from Ireland duty in March after he won 50 caps and represented his country at both Euro 2012 and 2016.
However, with first-choice left-back Enda Stevens suspended for Ireland's trip to Georgia, McCarthy will ask the Stoke City defender to step in.
"Stephen might tell me to get lost and he is retired," added McCarthy, who used midfielder Conor Hourihane at left-back against Bulgaria.
"But if I want him, he might just put his boots on one more time.
"James McClean is probably one of the best options if I don't have a recognised left-back.
"Hourihane had no chance at left-back ever. I played him to give him 65 minutes."