The Englishman sees his Millwall contract expire at the end of the season, and is said to be keen to leave The Den after a six-year stint.
Such news saw Newcastle United linked with the midfielder, who has registered three goals and three assists in eight Championship appearances so far this season, although they are said to face competition from West Ham United and Rangers in the battle for Wallace's signature.
According to Chronicle Live, the Scottish outfit have gained an advantage in the race for the 27-year-old, and could make an approach in January to see him arrive at Ibrox next summer upon the expiry of his Millwall deal.
Wallace hit 20 Championship goals in the last two seasons alongside 19 assists, making him a key target for the Magpies, who are yet to win any of their opening five Premier League games of the season.