The Liverpool-born multi-millionaire had hoped to inject cash into the club via a share issue.
A spokesman for Morgan said: "He has made a formal proposal which would result in a very significant injection of new capital into the club.
"That's been turned down. He now awaits the outcome of the board's strategic and financing review with interest."
It was initially thought that Morgan was mounting a takeover bid.
But on Monday he denied that and the club confirmed "that it is not in receipt of a takeover approach from any potential buyer."
With a 5% stake in Liverpool, Morgan is Liverpool's third biggest shareholder behind chairman David Moores (51% majority stake) and Granada (10%).
A share issue would have allowed Morgan to increase his stake in the club massively, maybe to as much as 15%.
The businessman is known to have wanted a seat on the board for some time and had hoped his investment (estimated to be £40-£50m) would be used to part-finance the new Stanley Park stadium and transfers.
Morgan was hugely critical of the financial package to fund the new stadium and he openly attacked Moores and the board at the January Annual General Meeting.
It was at that meeting that Moores finally agreed to discuss a partnership with Morgan.
Morgan made his fortune in the building trade and collected an estimated £240m from selling his stake in building firm Redrow Homes.
