The Frenchman would not be drawn on names, however, despite British media reports that Basel's Egyptian international midfielder Mohamed Elneny was set to become his first signing of 2016.
"You know more than I do. Unfortunately we cannot announce anything at the moment about this player because nothing has been concluded," Wenger told a news conference ahead of Saturday's home game against struggling Newcastle United.
"I will be busy, yes. I am already. I said already one month ago we are a bit short at the moment to deal with all the competitions we face, especially in midfield," he added. "We will be busy."
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Wenger needs cover in central midfield with Francis Coquelin, Santi Cazorla and Jack Wilshere all sidelined with injuries.
Arsenal, who went top on Monday after beating Bournemouth 2-0, are also without England striker Danny Welbeck.
Elneny has impressed at Basel and reports have suggested Arsenal have already agreed a fee with the Swiss side.
Southampton's Kenyan midfielder Victor Wanyama could be another target, having handed in a transfer request last summer, although the Saints are likely to resist.
Wenger indicated France international defender Mathieu Debuchy could be on his way out after being sidelined this season by injury and the emergence of youngster Hector Bellerin.
"It's not impossible," said Wenger of a player eager for playing time to win back his place in the national team ahead of the Euro 2016 tournament in France. "I'm happy if he stays but we'll see."
Arsenal, who are ahead of Leicester City only on goal difference going into the New Year, are chasing their first league title since 2004 but have looked fragile in an unpredictable season.
The Gunners were thrashed 4-0 at Southampton in the league last Saturday and only went through to the Champions League last 16, where they next face Barcelona, by the skin of their teeth.
"I am confident we will fight to stay there," said Wenger of the Premier League battle. "But it's a long way to go, we are just half way."
Wenger expected to have Chilean forward Alexis Sanchez, who picked up a hamstring injury at the end of November, back for the holders' FA Cup third round match against Sunderland on Jan. 9.
(Reporting by Alan Baldwin, editing by Sudipto Ganguly)
