France defender Koscielny has not featured for Arsenal since the 6-0 defeat at Chelsea last month following a calf injury, while Rosicky missed the FA Cup semi-final penalty shootout win over Wigan Athletic on Saturday due to a knock.
However, the duo could both be fit to feature as Arsenal return to Premier League action and aim to step up their bid for fourth place.
Wenger may be without Nacho Monreal, Alex Oxlade-Chamberlain and Lukas Podolski, though.
"We have plenty of uncertainties. We will have lots of tests today (Monday)," Wenger said ahead of the visit of Sam Allardyce's side.
"Rosicky and Koscielny will undergo tests today. Podolski, Ox and Monreal are also doubts."
Midfielder Jack Wilshere has been unavailable since the beginning of March because of a fractured foot sustained in England's 1-0 friendly win over Denmark.
But, according to Wenger, the 22-year-old is making good progress in his recovery.
"Jack Wilshere will start to run this week, he is progressing well," the Frenchman added.
Arsenal head into the game two points adrift of Everton, who moved into fourth place with a 1-0 win at Sunderland on Saturday.
And, with five games to play in the race for the final UEFA Champions League spot, Wenger has urged his side to move on from their dramatic FA Cup success and seal a much-needed Premier League win.
"Everybody is happy to qualify for the final. We must put it to the back of our minds now," he said.
"It's important to focus on the Premier League. We need to find our tempo for a derby game.
"We have a battle with Everton and we must be consistent until the end of the season."
