"I have not talked to anybody personally, but there are possibilities of contact," Chizik told reporters Tuesday.
He said he couldn't offer further details "because I don't have any."
Maryland fired coach Ralph Friedgen last week and there has been speculation that former Texas Tech coach Mike Leach would be the prime candidate to replace him.
Malzahn was a candidate for the Vanderbilt job but decided to stay with Auburn. He did not show up for a previously scheduled session with reporters after Tuesday's practice.
Malzahn has agreed to a three-year contract worth at least $1 million annually to stay at Auburn -- double his current salary. Bonuses could push his pay to $1.3 million.
When asked by ESPN's Scott Van Pelt about Maryland's interest in Malzahn, Chizik said he wants the best for his assistants -- and remembers when he was in the same circumstance as a defensive coordinator, trying to decide which coaching opportunities to pursue.
"It's a little bit of a catch-22 because obviously we want to keep intact our staff to the best of our ability," Chizik told Van Pelt. "We've got a great staff ... that's what makes it go at Auburn."
Although he wants the best for Malzahn, "Our goal is to also keep him in Auburn as long as we can and he's got to make those decisions," Chizik said.
Malzahn's fast-paced offense ranks sixth nationally in scoring and rushing and seventh in total yards per game. He also coaches Heisman Trophy-winning quarterback Cam Newton.
The Tigers are set to face Oregon for the national title Jan. 10 in Glendale, Ariz.
Malzahn has declined comment on the Vanderbilt job but said afterward that he wanted to be a head coach "somewhere down the line. If it's the right time, right place."
Meanwhile, SMU coach June Jones says he has no plans to leave for Maryland.
Jones says he spoke by phone with a search firm, but had no discussions with school officials from Maryland. He has removed his name from consideration for that job.
SMU players said Wednesday that Jones told them in a meeting about being contacted by Maryland representatives and his commitment to stay at SMU.
SMU is preparing for the Bell Helicopter Armed Forces Bowl Thursday against Army.
Information from The Associated Press was used in this report.