According to Sky News, Breedon contacted Marshalls earlier this year with an all-share takeover proposal. Marshalls, which has a market capitalisation of close to £400m, is understood to have rebuffed the approach.
There are not thought to be any live discussions taking place between the companies, Sky said.
Breedon has since pursued other acquisitions and announced the purchase of a limestone quarry in Missouri earlier this month for $120m.
A leading institutional shareholder told Sky the approach from Breedon to Marshalls had possessed industrial logic, and expressed surprise that it had not been made public.
At 1235 BST, Marshalls shares were 0.9% higher at 153p.
Marshalls declined to comment on Sky report.