The Reds are yet to tie the 20-year-old down to a new deal, and see Walcott as a potential replacement – particularly as he is embroiled in a contract wrangle of his own.
Walcott has found his first-team opportunities limited at the Emirates since returning from injury, but is nevertheless still looking for a rise on his £100,000-a-week wages.
But with less than 18 months to run on his current contract, Walcott could be moved on by manager Arsene Wenger, and according to the TelegraphLiverpool are waiting in the wings should such a situation arise.
The Reds reportedly enquired about Walcott before he signed his most recent Arsenal contract in 2013, but remain keen on the player, with his pace and directness making him a perfect fit for Brendan Rodgers’ side.
Any deal would likely depend on whether or not Liverpool qualify for the Champions League, but could still team Walcott up with Sterling should Mario Balotelli be moved on after a dismal season.