Middlesbrough, who are second bottom and seven points adrift of safety, will also be without defender Fabio Da Silva, who suffered concussion against Swansea City last weekend.
"With Gaston we're not sure, he had light training this morning and he's still out there with the medical staff as we speak," Agnew told reporters on Friday.
"Fabio won't be involved because of his concussion, and the seven-day ruling in place."
Defenders Calum Chambers and George Friend are both making their way back from long-term injuries, but neither will be available for the game.
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"It's difficult when good players, and players who have done well this season, are missing through injury, but this is football," Agnew added.
Middlesbrough need to beat Burnley and Agnew said the mood in the camp was positive.
"A lot of work has gone in from everybody, and we've had a good meeting this morning - the players are positive towards getting the three points we need," he said.
"Three points brings us closer and puts pressure on elsewhere. Confidence comes with results, and that's what we're aiming for. The fighting spirit is still there and it will be evident on the pitch."
(Reporting by Aditi Prakash; Editing by Andrew Bolton)
