The Sun says Gallagher is heading back to Blues after a season on loan at West Brom.
The 21-year-old has shone while at the Hawthorns despite their relegation struggle.
He has played 28 times in all competitions for the Baggies and confirmed his Premier League potential.
Gallagher's displays have caught admiring glances from elsewhere.
And a host of top-flight sides were hoping to secure his services for next season.
Crystal Palace are keen to bring the ace across the capital to Selhurst Park in the summer.
And Newcastle are also on alert to take him either permanently or on loan from Chelsea.
But Gallagher has other ideas and aims to force his way into boss Thomas Tuchel's plans.