The Spaniard star has been on McLeish's radar for a number of weeks and he was able to see him at close quarters at the weekend as the two clubs met in a pre-season friendly.
Gijon have already warned the Premier League club that they will not sell unless they get a decent bid.
Now after the goalless draw at St Andrews, where Michel impressed, McLeish admits the matter is now dependant on what finances he has available.
"I thought he was very comfortable. He's an elegant player with great athleticism," said McLeish.
"I will have to speak to the chairman and the board and see what the finances are."
McLeish has defensive issues going into the new season and has had former Liverpool defender Gregory Vignal on trial, and he is considering whether to make a move for him.
"I know exactly what he can bring us and he did himself no harm," said McLeish.
"He's still a player with Lens in France and we need to weigh up the situation."
He has also been linked with a move for free agent Sol Campbell as he looks to solve his defensive problems.
"It's been well known the problems at left-back, and we have been unfortunate with the centre-halves. Four of them are out at the moment," he said.
"The fans will be looking and thinking 'what's going on down there?'. It's not anyone's fault, it's extreme bad luck.
"I'm sure Man United, if they had four centre-halves out just now, would be saying the same thing. They would be in a crisis situation with their centre-halves because it's impossible to have six or seven in the squad."