Both played the full 90 minutes of the Republic’s 1-0 Nations League defeat to Wales on Sunday evening.
The rest of the squad and backroom staff returned negative test results before flying back to Dublin on Monday to begin preparations for Wednesday’s game against Bulgaria.
The news comes three days after midfielder Alan Browne tested positive.
Preston’s Browne had played against England at Wembley the day before his positive result, while another unnamed Republic player missed that game having tested positive two days before the game.
The Republic of Ireland’s squad has been depleted with the number of players ruled out from the original group now at 13 today.
Shamrock Rovers duo Graham Burke and Aaron McEneff are among four more players called up to the Republic of Ireland squad.
Former Under-21 player Jack Taylor of League 1 side Peterborough is also brought into the squad, while Troy Parrott has been promoted to the senior side from Jim Crawford’s group.
Burke has two caps recorded under Martin O’Neill from 2018, scoring against USA in a friendly.
McEneff, a 25-year-old midfielder and outstanding for the Hoops this season, played underage football with Northern Ireland, but chose to play for the Republic of Ireland several years ago.
The Football Association of Wales confirmed it is aware of Tottenham defender Doherty and Stoke midfielder McClean’s results, saying their preparations for Wednesday’s game against Finland remain unaffected.
“The FAW will continue to adhere to Public Health Wales and Uefa guidelines as well as internal protocols which have been implemented since the resumption of international football this year,” said a FAW spokesperson.
Republic of Ireland squad available on Wednesday as it stands:
Goalkeepers: Darren Randolph (West Ham United), Caoimhín Kelleher (Liverpool), Mark Travers (AFC Bournemouth)
Defenders: Kevin Long (Burnley), Shane Duffy (Celtic), Dara O’Shea (West Bromwich Albion), Cyrus Christie (Nottingham Forest), Ciaran Clark (Newcastle United), Darragh Lenihan (Blackburn Rovers), Ryan Manning (Swansea City).
Midfielders: Conor Hourihane (Aston Villa), Robbie Brady (Burnley), Jack Byrne (Shamrock Rovers), Jason Knight (Derby County), Josh Cullen (Anderlecht), Aaron McEneff (Shamrock Rovers), Jack Taylor (Peterborough United).
Attackers: Graham Burke (Shamrock Rovers), James Collins (Luton Town), Ronan Curtis (Portsmouth), Callum O’Dowda (Bristol City), Daryl Horgan (Wycombe Wanderers), Sean Maguire (Preston North End), Troy Parrott (Millwall, on loan from Tottenham Hotspur).