NewsAtDen has learned Lynch's financial demands, if met, would have put him at the top-end of the Lions' wage bill.
It is the second time in the space of 12 months Millwall have been thwarted in an attempt to sign the 24-year-old.
Lynch will become a free agent in June when his deal at the City Ground expires, although he has been offered a three-year extension by Forest manager Steve Cotterill.
Lions boss Kenny Jackett decided to switch his attention to other targets after big-spending Brighton became the latest side to come in for Lynch.
Jackett is chasing a new left-back as a matter of priority this summer and has also been linked with a move for Dundee United's Paul Dixon.