The newspaper claims in its live transfer blog (8:12am, Sunday 6 May) that the Scottish champions are now in the race for the 28-year-old.
It is understood that West Ham, Burnley and Wolves are already tracking the in-demand ace.
The report details that the versatile defender, who regularly switches between centre-back and right-back, is valued at £15million.
Dawson is expected to be one of several first teamers at West Brom to go through the exit doors in the summer, as Championship football looms.
Good move for Celtic?
Dawson would be an exceptional signing for Brendan Rodgers’ team in the summer and walk straight into the starting XI.
He has thrived as a centre-back in recent weeks during West Brom’s battle against relegation and unfortunately for them they may have left it too late in the day.
However, the English defender is entering the prime years of his career and the heading machine would be a force in the Scottish division.
The Bhoys need to continue improving their squad each year and his composing figure in the heart of their backline would be a positive step.
This Is Futbol rating: 9/10
Likely to happen?
It seems highly unlikely that Celtic will be able to pull off a deal for Dawson due to his price tag, while the fierce competition from English clubs would be tough to compete with.
This Is Futbol rating: 2/10