Dummett missed Newcastle's defeat to Leicester last weekend through injury but could return for Saturday's trip to Manchester United.
Wales face Spain in a friendly at the Principality Stadium in Cardiff on Thursday, 11th October before taking on Clark's Ireland in Dublin in the UEFA Nations League on Tuesday, 16th October. Before that, Ireland meet Denmark in the UEFA Nations League on Saturday, 13th October.
Clark has 32 caps for his country while Dummett won his third cap - against Ireland - last month after returning to the international fold under new manager Ryan Giggs.
His last cap had come against the Netherlands in November 2015 and last week, Dummett told NUFC TV in an in-depth interview: "When I was 17, I started going away with Wales (at youth and under-21 level). I've got a lot of Welsh family and my grandfather was Welsh, so that's where the connection came from.
"When (Chris) Coleman was manager, he selected me in the first team squad but I sort of travelled around a lot of times - I did miss a few through injury as well - but I never felt like I got the opportunity to play when he was manager.
"The time arose when I had a little bit of a niggle and I thought the best thing for me was not to go. He didn't like that and he told me that if I didn't go, he wouldn't select me again as long as he was manager. I knew from that day that I wasn't going to be playing as long as he was manager.
"He came out in the press and said I'd retired. I never, ever said I'd retired from international football - it was just that he told me that he wouldn't pick me anymore and it was his way of probably trying to make me look bad in the media.
"Obviously as everyone knows, he left to go and be the Sunderland manager, which didn't go too well, but when the new manager of Wales took over he gave me a call straight away and he let it be clear that he wanted me involved and wanted me to be part of the squad.
"At the time he called me, I didn't think it was the right time to go back - I'd just been injured for five months at the start of the season, when I got injured against Tottenham, and he fully understood my decision and he said the door will always be open, which was a different approach to what Chris Coleman had had.
"He understood, I think, from not only being a top level player but one who had not long retired. He understood the position I was in. I said I wanted to make sure I was fit for Newcastle because we were in the relegation zone at the time and ultimately I wanted to be playing Premier League football.
"Then the season finished, they went away on tour, and when the season started again they were back in contact and wanted me to go along again. I've been fit for quite a long time now and it was the right time for me to go back.
"He's given me my full (competitive) international debut now, which is obviously nice, and hopefully I can be involved more and get some more caps under my belt."
