Admittedly, swap deals rarely happen and there have already been denials, but Sanchez's work ethic and versatility across the frontline could be ideal for Pep Guardiola. Aguero's deadly finishing skills, meanwhile, are what Arsene Wenger has been missing ever since he sold Robin van Persie to Manchester United in the summer of 2012.

A swap of South American stars could solve significant questions for both managers. While both clubs would lose a fan favorite in the deal, they'd be bringing in experienced replacements with enough talent and magnetism to render their predecessors a fond memory in the minds of supporters.

With Wenger agreeing to stay for two more years, the outstanding item in his in-tray remains the futures of Sanchez and Mesut Ozil. Both of his two most expensive signings have just a year remaining on their contracts, and will be able to sign pre-contracts for new clubs beginning in January.

A member of Chile's national team, Sanchez headed to the Confederations Cup in Russia with little sign of having come to an agreement with Arsenal. Instead, his name has been linked with a host of suitors that include City, Manchester United, Paris Saint-Germain and Bayern Munich. Though he starred in Arsenal's defeat of Chelsea in the FA Cup final and scored the first goal of the 2-1 win, there were public signs throughout last season that all was not well.

On-field tantrums following a 3-3 draw at Bournemouth in January, and similar frustration during that 10-2 punishment administered by Bayern Munich in the Champions League, suggested the Chilean star was not blissfully happy. While he is known to enjoy life in London, Sanchez is not a great mixer with his colleagues, though that has been his habit throughout his career.

Despite his quirks, losing Sanchez this summer would deal Wenger's credibility a heavy blow -- especially after the manager's own contract extension did not receive universal approval from Arsenal fans. Starting the season badly without Sanchez would undoubtedly lead to the Emirates ringing out with dissent once again, and would cause Arsenal Fan TV to spring into frenzied overdrive.

After guiding his team to a disappointing third-place finish last season with no trophies to show for it, Guardiola should expect protest if Aguero were allowed to leave. So too should chairman Khaldoon Al Mubarak, who declared in May there had "never been a doubt" that Aguero could leave Manchester.

The sentiment rather flew in the face of that spell in January and February when Aguero was benched in favour of Gabriel Jesus, who very much looked Guardiola's chosen one during a stretch when City played the brand of Barcelona-style football that the Catalan genius was supposed to bring to the Etihad. Jesus' willingness to work back in midfield and press the opposition seemed a far better fit for Guardiola's system than Aguero, who previously preferred to conserve his energy for his self-possessed pursuit of goals.

Sergio Aguero and Alexis Sanchez have been linked with moves away from their respective clubs. Getty Images

Had Jesus not suffered a fractured metatarsal at Bournemouth in February, and Aguero not reclaimed his starting place to then score 15 goals in 19 matches while also increasing his work rate, then the striker's future would be more uncertain.

"He will be here next season," said Guardiola after City's final match of the season. "Happy? Good. Perfect."

Guardiola would surely enjoy adding Sanchez to his forward line; the Chilean offers similar variety and industry to Jesus from the wings as well as the central position, where he impressed during the first half of last season.

When the pair worked together previously during Guardiola's final season at Barcelona (2011-2012), Sanchez faded in the imposing wake of Lionel Messi. However, if Aguero was not around, the Chilean should find it easier to flourish.

Even if Arsenal complete the signing of Alexandre Lacazette from Lyon this year, Aguero would be undisputed first choice at the Emirates. His supreme ability to capitalize on the multitude of chances his hypothetical new team is capable of creating in a given match could haul Arsenal back into the top four at least.

For Wenger -- who has just two years on his own deal-- moving on Aguero could offset the problematic situation of a manager deciding to phase out a leading man whose presence on the bench will always incite skepticism and questions.

It will almost certainly never happen, but an Aguero-Sanchez swap would make significant sense.