The Argentine’s expiring Manchester City contract will not be renewed, bringing to an end an illustrious, trophy-laden decade-long stint in which he became the club’s all-time leading goalscorer.
Aguero’s popularity and standing at City is such that a statue in his honour is set to be commissioned at the Etihad Stadium by chairman Khaldoon Al Mubarak to go alongside the ones currently being developed to celebrate fellow club legends Vincent Kompany and David Silva.
The 32-year-old has insisted he wants to remain playing at the “highest level” after leaving City, with Chelsea and Arsenal already rumoured as possible suitors alongside the likes of Juventus, former club Atletico Madrid, Paris Saint-Germain and Inter Milan.
United are also likely to be in the market for a new forward this summer, particularly with a decision yet to be made on the future of Edinson Cavani, but Solskjaer does not see Aguero treading a similar path to the likes of Carlos Tevez by crossing the Manchester divide.
The list of players to have turned out for both clubs also includes the likes of Peter Schmeichel, Andy Cole, Andrei Kanchelskis and Owen Hargreaves, but it’s not something the Norwegian typically supports.
"I wouldn't expect any player who has played for a club for 10 years to want to go to their local rivals," Solskjaer said ahead of Sunday night’s Premier League visit of Brighton to Old Trafford.
"I know we're professionals, but when you play for Man United you don't go to Man City. We've had examples of that and I didn't really agree with it.
"When I played for Man United, if a rival club tried to sign me, and I had gone - well, where's the loyalty? Loyalty is one of the values I really, really put highly."