The left-sided midfielder has endured a turbulent time since joining the Reds for £20 million in the summer of 2011 and has failed to break into manager Brendan Rodgers' first-team plans.
And, while Mowbray suggests it would be difficult to engineer a way back to former club Boro for Downing, he admits that he would jump at the chance were a deal plausible.
"I don't want to talk about [Downing], he's a Liverpool player," the 48-year-old told the Northern Echo.
|5/4||Middlesbrough are 5/4 with Bet365 to score under 1.5 goals against Bristol City|
"He is an international footballer, we are Middlesbrough in the Championship, who have been selling players for the last two years.
"We have reduced the wage bill from £27m down to £12m, £15m off it, gone. That's where we are.
"And if I was a Premier League manager, why wouldn't I want Stewart Downing? Half the league would want him."
Downing made more than 230 appearances for Middlesbrough before moving to Aston Villa in 2009. He has scored two goals this season for Liverpool, both in the Europa League.