Mertesacker has just 17 months to run on his current deal while Sagna is already free to sign a pre-contract agreement elsewhere.
Both have been cornerstones of an Arsenal defence which has as good a record as any in this season's Premier League.
And, speaking at his press conference ahead of Saturday's game against Fulham, Wenger appeared confident of keeping both.
He said: "We are making good progress, and hopefully we can announce something soon."
The Arsenal manager was a little more coy when asked about the possibility of a deal for Schalke's Germany international Julian Draxler.
Some reports this week even suggested Draxler had been spotted at the club's training ground, but Wenger said: "It's like UFOs - some see them everywhere!
"The transfer window is open until January 31. Are we close to signing anybody? At the moment I would say no."
Wenger denied making a bid for Dimitar Berbatov, who is likely to lead the Fulham attack at the Emirates, and offered no public update on his own contract situation.
There was a hint, though, that he has already decided whether or not to extend his spell in charge beyond the summer.
He said: "You can make a decision without going public. You can take that sentence how you want."