The Daily Star says Real last night claimed Liverpool were negotiating with them for £15m-rated Gago.
Reds director of football Damien Comolli is believed to have already opened talks with Gago's agent Marcelo Lombilla over the possible move.
Lombilla said: "Gago needs to play and Liverpool would be a perfect club for him, Fernando wants to get back on the pitch and return to the top level and at the moment that is not possible in Madrid."
Liverpool had positive reports on Gago earlier in the season.
A source at Madrid said last night: "Fernando knows that he has no future at the club.