Stewart is out of favour with the Robins, who he joined in the summer, and does not appear to be in the future plans of new boss Gary Johnson.
And Lee is hoping to lure him to the Lions, who currently sit bottom of the Championship.
He said: "If Marcus doesn’t feature in the starting line-up at Bristol City very soon, we might have a good chance of bringing him here.
"To get out of our current situation we have to score more goals, and Marcus fits the bill. Bristol City allowed us to talk to the player, and it's now up to him.
"Marcus has a good goalscoring record, and he is finding it difficult to come to terms with not being in the long-term plans of their manager."