The 14-goal forward missed the 2-1 win at Fulham with the ankle injury he suffered at Reading, but Laudrup had hoped he may be ready to face Paul Lambert's beleaguered side.
Swansea made light of the absence of the converted striker at Craven Cottage, with Danny Graham deputising and opening the scoring.
But, given the impact Michu has made since his arrival from Rayo Vallecano, Laudrup is understandably keen to have him fit, and he will have a late fitness test to determine his availability.
Laudrup said: "I don't know if he will be fit.
"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."
Swansea will face a Villa side short on confidence after a nightmare run of defeats against Chelsea, Tottenham and Wigan over the festive period.
The Villans have conceded 15 goals and scored none during that sequence, and are just above the relegation places.
But Paul Lambert has emerged victorious in each of his three fixtures against the Swans as a Premier League manager, and the hosts will not be taking Villa lightly, according to striker Graham.
He said: "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."
Despite his goal at Fulham, his fourth of the season, Graham has been linked with a move away from the Liberty Stadium, although the former Watford forward has made it clear he wants to continue with the Swans, as long as Laudrup is happy for him to stay.
One of the reasons for Graham's desire to remain at the club is the manner in which Laudrup has taken Swansea forward after replacing Brendan Rodgers.
And Graham believes the improvements the Dane has made to the attacking side of the Welsh club's game make it the ideal place for a striker to be.
"I think we're a better side. I think we attack a lot more, get more goals, a lot more chances in the game," he said.
"The gaffer wants us to get forward and take chances and that's been beneficial to the team and a number of players so hopefully it can continue over the next half of the season.
"We've got a good squad now and anyone who comes in can do a job in the team.
"I'm sure that gives the gaffer a pleasant headache, to make seven changes and win a Premier League game away from home just shows the strength in depth we have now.
"Everyone's excited for January, the New Year and what 2013 will bring for us."