Downing's arrival would be a major boost to Boro's bid to return to the Premier League. And with the Football League loan deadline not until Thursday night, boss Tony Mowbray was hoping to get him now.
But Kop boss Brendan Rodgers must replace the 28-year-old and move others in and out - so the move may not happen until January.
A source close to Downing told The Sun: "He'd love to help Boro and Mowbray will do everything to make it happen."
Cash-strapped Boro will need Liverpool to pay most of his £80,000-a-week wages.