The council wrote to firms last week asking to be compensated following the Office of Fair Trading's (OFT) investigation.
Companies named by the Office of Fair Trading as being engaged in cover pricing in the Leeds area include Caddick, Carillion, Henry Boot, P Casey and Strata.
But the council declined to reveal which firms it has written to.
A statement from the authority said that in addition to seeking compensation it would consider "further courses of action should it prove necessary".
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