City announced on Tuesday that their all-time record goalscorer will leave the club at the end of this season when his contract expires.
The last high-profile player to join City from United was Aguero's former Argentina teammate Carlos Tevez, who spent two seasons on loan at United before joining rivals City in 2009 and won the league title in the 2011-12 season.
Solskjaer has said he does not expect Aguero to follow in Tevez's footsteps this summer.
"I wouldn't expect any player who has played for a club for 10 years to want to go to their local rivals," Solskjaer told reporters.
"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."
Over 40 players have represented both Manchester clubs, with Andrew Cole, Owen Hargreaves and Peter Schmeichel among the players from the Premier League era to have moved from United to City.
United return to league action on Sunday when they welcome Brighton to Old Trafford. Solskjaer's side are second in the table and 17 points behind City who have played two games more.