The in-form striker, who has scored 14 goals this season, sustained an ankle injury in the recent match with Reading.
Laudrup challenged his players to overcome Michu's absence when they travelled to Fulham at the weekend, and they delivered by earning a 2-1 victory.
And the Swans manager hinted he may have to ask his charges to repeat the feat when struggling Villa arrive at the Liberty Stadium.
"I don't know if he will be fit," Laudrup said. "Obviously, he got an injury on his ankle and it was twice the size the other day.
"It's not a muscle injury but it's a question about pain and if he can't put his foot into the boot then he can't play. He can't play in bare feet, I don't think.
"The medical team say it's a possibility he could be fit for Tuesday but let's see."
Laudrup has warned his team against complacency as well, with Villa on a run of three defeats that has seen them concede 15 goals to Chelsea, Tottenham and Wigan.
He added: "It's been a difficult time for Aston Villa - everyone's going to be down. But it's a football game, we have to respect them.
"It's going to be a tough game but we're going to be looking to build on what we've done at Fulham and hopefully get another three points on New Year's Day."