Hajime Moriyasu is concerned about his winger, who suffered a hamstring injury in his club’s 3-0 win over Wolves.
But he was unable to give any definitive guidance on how things stand.
Japan will be worried about Mitoma with a view to this summer’s World Cup finals.
Albion’s thoughts will be on remaining Premier League games against Leeds and Manchester United.
Mitoma has looked pleasingly fit, strong and sharp in recent matches.
But he went down clutching the back of his left thigh as he chased the ball towards the byline.
There was a lengthy stoppage for treatment and a stretcher was readied.
But Mitoma was able to limp away unaided, which was seen as mildly reassuring, in the company of medical staff.
He left the stadium on crutches and did not do his customary interviews with Japanese reporters.
Moriyasu told reporters in Japan: “I haven’t yet received any definitive information.
“What the club staff have told me is that, at this stage, they still don’t know how long the recovery period for the injury might be.
“We’re hoping it turns out to be a minor issue but the impression I’m hearing from them is that it may not be a minor injury.”
Leeds’ side includes Mitoma’s childhood friend Ao Tanaka.
They were unable to go up against each other at the Amex because Mitoma was out injured.