"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."
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.
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 zone. But 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.
"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," he said. "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."