Liverpool are likely to attempt to offload the 28-year-old, who joined the Reds in a £20million (€24m) switch from Aston Villa in July last year, in January with Rodgers keen to address his lack of strike-power.
There is interest from a series of Barclays Premier League rivals in a permanent move but Downing is understood to still be determined to prove he has a long-term future on Merseyside.
In the circumstances, the player would prefer a temporary move, and his former employers would provide a tempting alternative.
Boro, who currently lie in third place in the npower Championship, were not commenting publicly on the matter today, but sources on Teesside have indicated that nothing is likely to happen ahead of Thursday's emergency loan deadline.
But January would provide an opportunity to resolve a situation which bears a striking resemblance to that in which striker Andy Carroll found himself.
The £35million frontman was surplus to requirements during the summer, but had let it be known he was willing to consider a temporary move back to Newcastle, the club which had raked in a fee since described by manager Alan Pardew as "astronomical" for their home-grown talent.
However, while Newcastle would have been able to fund a sizeable percentage of Carroll's wage packet, Boro would need Liverpool to pick up a large part of the tab for Downing, and that could prove a stumbling block even if they were willing to enter into an agreement.
Downing, who emerged through the ranks on Teesside before winning a transfer to Aston Villa in July 2009, has managed 14 senior appearances this season, although most of his starts have come in Europe.
In addition, he has found himself at times employed at left-back rather than on the wing with teenager Raheem Sterling having taken over his mantle.