City confirmed on Monday that Aguero is to bring an end to his decade-long spell at the Etihad Stadium when his contract expires at the end of the campaign.
He will bow out as City's all-time leading scorer, with a current tally of 257 goals in 385 games, the most recent of those appearances coming against Leicester City on Saturday.
But despite the Premier League's fourth-highest ever goalscorer being available on a free transfer, Solskjaer does not expect Aguero to join one of the Citizens' domestic rivals.
"When I played for Man Utd, if a rival club would try to sign me and I'd gone to a rival club, where's the loyalty?" Solskjaer said.
"Of course, loyalty is one of the values I rank highly."