Reds manager Rafael Benitez is reportedly ready to offer Boro £12 million for the services of the talented left winger.
Tottenham Hotspur are also interested in acquiring the 24-year-old's services, and have had several bids for the player turned down by Boro, but Downing is now apparently ready to move on from the Riverside, and the list of clubs interested in him is growing by the day.
Spurs have already failed with bids during this transfer window and have now seen Downing's transfer request as their opportunity to pounce for the England international.
Liverpool bought Albert Riera during the summer transfer window and already have Ryan Babel in their squad, but Benitez seemingly wants Downing as a squad player, which he will inevitably be should he move there.
Downing has been playing for Boro for his entire professional career, only playing seven games for another team, at Sunderland during a loan spell in 2003.
Since he was promoted from the infamous Middlesbrough youth team, the 24-year-old has made a total of 154 Premier League appearances and scored 17 times in the process.