Sunderland team and injury news ahead of Carabao Cup quarter final against Arsenal
Dajaku was forced off in the first half of the 1-1 draw with Ipswich Town after picking up an injury from a firm Sam Morsy challenge.
The 20-year-old left the pitch on a stretcher and while Johnson hopes it will not lead to a lengthy absence, he is unlikely to be involved at the Emirates.
It is expected, though, that Corry Evans will make his return from a thigh injury.
Sunderland have one confirmed further absentee for the game due to a positive COVID-19 test result, but with no close contacts identified the rest of the squad is at this stage not affected.
The squad will test again on Tuesday morning before travelling.
Arsenal currently have two confirmed cases of COVID-19, with Pablo Mari and Albert Sambi Lokonga both recently missing fixtures.
“We’re giving Leon every chance,” Johnson said.
“We’ll probably X-ray it as he’s still a bit sore, but it’s a contact injury so we’ll give him every chance to be available.
“But I wouldn’t be putting too much hope on that one.
“We do have a few little niggles, so we will be missing at least one with the positive COVID-19 result as well.
“Corry Evans is in the squad for the game.”
Dennis Cirkin remains on track to return to make his return from a double hernia over the festive period, though it is not yet known whether he will involved at Arsenal.