West Bromâ€™s slim hopes of Premier League survival were destroyed last night following Southamptonâ€™s 1-0 win over Swansea.
And according to the Daily Mail, Dawson could be on his way out of West Brom this summer as they prepare for Championship football.
Dawson joined West Brom in 2010 from Rochdale and has gone on to make 179 appearances for the Baggies.
The versatile defender, who can play as a centre-half as well as right-back, would be available for around ÂŁ15m.
â€śNewcastle and Celtic want West Brom defender Jonny Evansâ€ť
Dawsonâ€™s team-mate and fellow defender Jonny Evans is also expected to spark a transfer battle in the summer.
The Albion captain has been linked with the likes of Arsenal, Manchester City an Leicester over the past couple of windows.
And due to a relegation release clause in his contract, the Northern Ireland international will be available for just ÂŁ3m.
West Brom left-back Kieran Gibbs apologised to the supporters after their relegation was confirmed.
The Baggies kept their survival hopes alive under caretaker manager Darren Moore, who was named Premier League Manager of the Month following an unbeaten run of five games.
Gibbs posted on Twitter: “Horrible feeling to be relegated, especially after our recent form as a team!
â€śIt’s been a wild season on and off the pitch and has been a huge learning curve.
â€śWhatever has gone on this season there are no excuses we haven’t been good enough for the majority of it.
“For that we are sorry to the W.B.A fans who have been quite unbelievable considering the circumstances. Thank you for your amazing support this season!”