Tottenham and Fulham are keen on the 20-year-old but reports on Saturday morning suggest that Middlesbrough have put in place a deal worth up to £2m to seal Dawson's signature.
Having moved to Spotland from Radcliffe Borough, Dawson played a key role in Rochdale's promotion this season with commanding performances at the back and a valuable tally of 9 league goals.
Also on his way is Shrewsbury Town striker Dave Hibbert, with Peterborough set to offer the out-of-contract player a deal for next season.