The Mirror says Wenger will step up his bid to sign 15-year-old wonderkid Sterling next month - to stave off interest from a host of other clubs.
The Arsenal boss has had the lightning-quick QPR striker - rated as highly as the young Wayne Rooney - watched on several occasions, including Rangers' reserve game against Aldershot earlier this month, which finished in a 2-2 draw.
Since that match Sterling, who turned 15 on December 8, has been promoted to training with the west London club's first team.
Rangers had been ready to make him the youngest first-teamer in their history in order to ward off the Premier League big guns.
But the change of management which has seen Jim Magilton replaced by Paul Hart, plus the bad weather, has seen his debut shelved.