Gallagher, 25, initially impressed when he joined the Spanish giants but has since fallen down the pecking order under Diego Simeone.
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The central midfielder has started just four of his 19 La Liga games so far this season, popping up with two goals as Atletico sit in fourth.
Aston Villa have been heavily linked with a move for Gallagher as they seek to maintain their push for Champions League qualification.
According to The Mirror, Gallagher is "interested in what Aston Villa have to offer” and would be willing to make the move.
It’s understood that Atletico are unwilling to let him leave on a straight loan, however, so a move would have to be permanent or include an obligation to buy.