The Belgium midfielder suffered a hamstring problem in the recent 1-0 win over Tottenham and is yet to make a full recovery.
Pep Guardiola says his condition is improving, but admits Sunday's game will arrive too soon for him to be involved.
Meanwhile, Fernandinho faces a late fitness test to see if he is fit enough to play after suffering a knee injury in the win over Manchester United on Wednesday.
“Still Kevin is not fit,” Guardiola said. “He’s getting better, but is not fit.
“We will see tomorrow [if Fernandinho is fit]. He had a problem in the knee, but we will see tomorrow.”
Sunday’s game against Burnley represents another crucial juncture in this season’s title race.
In one of the most keenly contested battles for the Premier League in recent history, City currently sit one point ahead of Liverpool with three matches remaining.
Win them all and we will become the first side in a decade to win back-to-back Premier Leagues.
Guardiola says he knows it will be a tough afternoon at Turf Moor against a side who pose specific challenges, but feels confident his players know exactly how to combat them.
“Always is [hard to play at Burnley],” he said. “They do really well what they do.
"We have to prepare and we are prepared. It’s the end of the season - the last games - and everyone feels pressure.
“Today we have day off and then we prepare for Burnley’s tough points.”