Cooper was forced to miss the weekend's 2-0 win at Huddersfield Town with the calf problem and the captain also sat out Tuesday night's 2-0 win at home to Hull City.
But Whites head coach Marcelo Bielsa has revealed that Cooper is now close to making a return though the defender will not be risked unless he is 100 per cent.
"Cooper is much better," said Bielsa.
"And the rest of the injured players are not available - I am talking about Shackleton and Tyler Roberts. (and Adam Forshaw).
"If there is any risk that Liam is not going to be 100 per cent we are not going to consider him."