The Frenchman missed the Magpies’ 1-1 draw at West Ham United last weekend due to a calf problem.
He returned to France this week where he has been undergoing “ intensive, specialised treatment”.
Head coach Eddie Howe hopes to have the 24-year-old at his disposal as United look to climb above the Bees in the Premier League table with three points.
Meanwhile, Ryan Fraser is set to feature after Howe confirmed the Scot “will be OK” despite limping off at the London Stadium.
Javier Manquillo, injured in the same game as Kieran Trippier, has returned to training but isn’t fully fit yet, suggesting Emil Krafth will retain his place at right-back.
“Saint-Maximin, we’ll make a late call on,” Howe said
“He’s been away getting intensive treatment. We said when he suffered the injury it wouldn’t be long-term so we’re keeping our fingers crossed on him.
“He got a bang on the calf against Aston Villa.
“In terms of his rehab, he’s been away to get intensive, specialised treatment abroad. We felt that was the quickest way to get him fit.
“He’s in a very good place mentally and eager to return.
“Ryan Fraser will be OK. He came off the pitch against West Ham but it looks like he’ll be fine.
“We’ve had a bit of illness in the camp this week but nothing too serious.
“Manny came through a couple of training sessions this week.
“I wouldn’t say he was 100% fit but he’s certainly getting closer to being fit and available.”
Callum Wilson and Trippier - both long-terms injuries remain sidelined, as is Matt Ritchie, who is recovering from a knee injury.