West Bromwich Albion
The newspaper claims that Burnley have already had a bid of an unspecified amount rejected by West Brom, who are said to be seeking £15m for the former Rochdale man.
The Daily Telegraph separately reports that West Ham have been met with rejection after offering £12m for Dawson, 28.
West Brom have already been forced to let Jonny Evans go for just £3m since their relegation, with Leicester triggering a newly active release clause for the Northern Ireland international, who had previously been linked with move to Arsenal or Manchester City for upwards of £20m.
Capable of playing at both right-back and centre-back, Dawson joined the Baggies in 2011 for less than £300,000. He has since played close to 200 games for the club, including finishing just 35 minutes shy of being a Premier League ever present during the 2015/6 season.
As things stand, he remains under contract at the Hawthorns until the summer of 2020.