Arsenal have been short on defenders all season with Thomas Vermaelen out long-term and all of the club's other senior defenders having been sidelined at some point.
Wenger had said he was looking to sign a new centre-back in January, but with just six days to go before the transfer window slams shut he is no nearer to bringing anyone in.
Woodgate has made just three appearances since the start of the 2009-10 season and was left out of Tottenham's squad for the first half of the season due to his injury problems.
"That was not on our mind at all, completely out of the blue,'' Wenger said. "I like Woodgate as a player, but we are not after him. "We are nowhere near (signing a central defender). At the moment I am not too confident.''