An exchange of the two players could be an unlikely, but spectacular swap deal that could actually work out best for everyone.
The former Gunner told Sky Sports that he thought such a deal would be a fantastic piece of business for Liverpool, but it may be just as good for Arsenal, and even more importantly, for both players.
Liverpool winger Sterling's future is up in the air, with contract negotiations at somewhat of a standoff until the end of the season. There is speculation that he could to be open to leaving if the Reds fail to secure Champions League football. At the Gunners, Sterling's England teammate Walcott is at a side bang in form, but faces an entirely different dilemma.
Walcott failed to feature, let alone start, against Burnley at the weekend, ensuring he remains on the periphery of the Arsenal first team.
Sterling is surely set to feature against Newcastle on Monday night for Liverpool, and were any deal to go ahead it is this fact, that the England international is playing regularly for his club, coupled with his younger age, that would likely mean Arsenal would also have to include some money alongside Walcott in order to sign Sterling.
On one hand, it is completely understandable that Arsene Wenger is reluctant to alter his starting lineup by including Walcott, with the Gunners on a fantastic eight-match winning streak in the Premier League. But the ex-Southampton player has had a playable level of fitness for a few months now after his knee injury, without managing to impact the Frenchman's starting lineup, and moving into what should be the prime of his career, he would be eager to be involved more regularly.
Looking at what the two players could offer their new clubs also seems to support a possible switch. Sterling is a more skilful and inventive player than the older Walcott, and is stronger and more tenacious both in and out of possession. This is a feature of several other Arsenal wingers, with Alexis Sanchez and Alex Oxlade-Chamberlain both difficult to dispossess and capable of offering something defensively. He is young enough still to be incorporated into another side's methods, considering he will not turn 21 until November.
Where Walcott impresses is his directness and goalscoring potential, and as a proven player of Premier League class, where his very best form is arguably better than Sterling has managed in his young career, it is likely he would be a fine swap if the former QPR man would want a move away from Liverpool.
For the Reds, Walcott could also find himself employed in a central position - something that would likely greatly appeal to him. With Sterling, Brendan Rodgers has already shown that he is prepared to move his wingers inside in order to try them as strikers, while Liverpool's forwards are also happy to come at the defence from wide areas. Walcott would be a very suitable option in this regard.
The drawbacks for Liverpool would be that Sterling's potential is still hard to pinpoint. Certainly he looks like being a very good player, capable of having a strong top level career, but he may be capable of more than that, with the chance of becoming one of Europe's best wingers also a strong possibility. The Reds and Brendan Rodgers would surely be reluctant to let any player push to leave Liverpool for Arsenal, one of their direct rivals and a club at the position they are trying to achieve (with regards to regular Champions League football), let alone one of their most promising.
For Arsenal, there would be question marks about whether Sterling would get in the current side, given their good form and similarities between the two players. How much would the acquisition of Sterling in place of Walcott actually improve the present side and squad at the Emirates? He may be a player of great potential, but the best way for him to reach that is to get regular game time.
Either way, the two players, not to mention their clubs, could do a lot worse than entertaining the idea of a swap, especially if Arsenal are willing to include some money to sweeten the deal.
But what do Arsenal and Liverpool fans think?