The Gunners have been linked with moves for the trio before the transfer window closes, but the Frenchman insists that none of them are currently on his radar
England international Welbeck, who Goal understands has asked for showdown talks with United manager Louis van Gaal, could be offloaded before the window closes while Barcelona midfielder Song has been tipped to leave the Liga giants in the coming days.
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When asked about Falcao, Wenger insisted the former Porto striker was not in his price range and revealed that Welbeck was also not a target for the Gunners. As for a possible deal for Song, the Frenchman said: "Alex Song will not be coming back."
Olivier Giroud is set to be out for around four months after undergoing surgery on a broken tibia, although Wenger is convinced that Alexis Sanchez is capable of leading the line in his absence.
The Gunners boss said of the Chile international, who struck the winning goal in Wednesday's Champions League play-off victory over Besiktas: "[Can Alexis play up front for] three or four months? He can play there his whole life.
"I bought him to play as a striker, not to play only on the flanks. I believe you cannot everytime buy when a player is injured."
When asked if Arsenal would be signing a defender or midfielder, Wenger said: "We are open for any position as long as we feel that the player can strengthen the squad.
"Buy to buy, I don't see the purpose of that. If we find the players who we feel can give something to our squad, we will do it in any position. We are open but it has to be enough to buy. It has to make sense."