Naismith, who won the last of his 49 caps against Portugal in October last year, has been beset by injury problems and this term the 32-year-old forward has not played a full 90 minutes for Scottish Premiership side Hearts.
West Ham defender Snodgrass, 31, has not featured in a Scotland side since coming on as a substitute for his 26th cap in the 4-0 hammering by Belgium in a friendly in September 2018.
"He has good experience, Robert," said Clarke.
"When I spoke to him over the summer he was very keen to come back on board.
"He picked up a little injury last week but he let us know he was fine."
Despite the size of the task facing Scotland, who have conceded seven goals without scoring against Belgium in their last two outings, Clarke decided to give striker Leigh Griffiths more time to reintegrate into the Celtic team.
Griffiths missed the last six months of the 2018/19 campaign to deal with mental health problems but has scored three goals this season and said he was ready to return for Scotland.
"He was close," Clarke said.
"Leigh has got some fantastic attributes. I just look at him just now and he's come a long way in a short space of time after a very difficult spell in his life.
"And I feel we should just give him a little more time to settle into the role again at Celtic and get himself fully fit and firing. And a fully fit and firing, sharp Leigh Griffiths will always be good for us.
"But at the moment I just feel it's a little bit too early to push him."
Scotland made a woeful start in their Euro qualifying campaign under Clarke's predecessor Alex McLeish, having been hammered by Kazakhstan and Belgium, the number one ranked side in the world.
Scotland are fourth in their group, level on six points from a possible 12 with Kazakhstan, six points behind leaders Belgium.
The Scots host Russia, who are second in the group with nine points, on September 6, and the Belgians three days later.
Goalkeepers: Craig MacGillivray (Portsmouth/ENG), David Marshall (Wigan Athletic/ENG), Jon McLaughlin (Sunderland/ENG)
Defenders: Liam Cooper (Leeds United/ENG), Grant Hanley (Norwich City/ENG), Charlie Mulgrew (Wigan Athletic/ENG), Stephen O'Donnell (Kilmarnock), Liam Palmer (Sheffield Wednesday/ENG), Andrew Robertson (Liverpool/ENG), Greg Taylor (Kilmarnock)
Midfielders: Stuart Armstrong (Southampton/ENG), Ryan Christie (Celtic), Ryan Jack (Rangers), John McGinn (Aston Villa/ENG), Callum McGregor (Celtic), Kenny McLean (Norwich City/ENG), Robert Snodgrass (West Ham United/ENG), Scott McTominay (Manchester United/ENG)
Forwards: James Forrest (Celtic), Ryan Fraser (Bournemouth/ENG), Oliver McBurnie (Sheffield United/ENG), Steven Naismith (Hearts), Matt Phillips (West Bromwich Albion/ENG), Johnny Russell (Sporting Kansas City/USA)