Walcott, like his current captain Robin van Persie, has one year remaining on his contract with Arsenal and his uncertain situation has led to speculation the 23-year-old's time at the Emirates Stadium may be edging towards its conclusion.
Liverpool, it is claimed, are vying alongside Chelsea and Paris Saint-Germain for Walcott, and Rodgers is said to be 'desperate' to capture the England international before the start of the new season.
There have been mutterings and murmurings for some time regarding the future of Walcott as an Arsenal player but an official approach from Liverpool would still arrive as somewhat of a surprise.
Should Liverpool formalise their supposed interest then Arsenal would be presented with a proposal that leaves Arsene Wenger in an apparent quandary.
Walcott's position at Arsenal is not one so concrete that the Gunners would reject offers without consideration as they would have done with Van Persie prior to his contract dispute.
And, with Liverpool reportedly prepared to offer in the region of £15 million for Walcott, perhaps Arsenal would be best advised to sell a player who encourages the exhalation of more frustration than adulation.
However, Walcott's performances last season showed that he has added greater penetration to his industry, as the statistics will verify, and perhaps suggest he is on the cusp of realising his potential.
But will this potential be fulfilled away from Arsenal? Wenger's decision, should any suitors come calling, will be pivotal in Walcott's career.
Stay and Walcott must prove he is worthy or a regular starting place ahead of Alex Oxlade-Chamberlain. Leave and he may be afforded the opportunity to play more regularly in his favoured central position.
A move to Liverpool could suit Walcott perfectly at this stage in his career, and he would surely flourish at Anfield given the lowered expectations of a club in transition under a young manager.
The influence of the fans on the performance of player cannot be underestimated either, and Liverpool supporters are known for their patience - something not always spared for Walcott in north London.
One's personal experience in attendance at the Emirates Stadium has made it clear that no Arsenal player attracts the ire of the club's fans more than Walcott, albeit more fuelled by expectation on someone who, it was hoped, would be a world beater by now.
Walcott would benefit from beginning next season with a clean slate and, given that Liverpool are looking forward and not back under Rodgers, it could be the ideal fit for the former Southampton attacker.
Rodgers may find his interest immediately rebuffed by Wenger, and Arsenal strive to tie Walcott down to a new long-term contract rather than entertain the idea of moving him on.
But, whatever transpires over the coming few weeks, next season will be crucial in the faltering career of Theo Walcott.