The Catalan boss attempted to sign the Lyon forward last summer but was unable to get a deal over the line.
Koeman worked with the 27-year-old whilst in charge of the Netherlands and is keen on a reunion.
Depay, like Aguero, would be available on a free so the finances would not impact on either deal.
Aguero has been plagued by injuries this term, but at 32 still has plenty to offer.
He is also good friends with Barcelona star Lionel Messi which could prove advantageous.
City have announced that the forward, who scored their historic title winning goal in 2012, will have a statue erected outside of the Etihad.
He also feels that the Dutchman would be more willing to accept a substitute role from time to time as he rotates his squad.
Depay has continued to find the net with regularity at the Groupama Stadium as Lyon push for the Ligue 1 title.
Barcelona, for all their recent struggles, have several promising young players at their disposal and shrewd recruitment this summer could set them up nicely for the future.
There is growing optimism that Messi will remain at the Nou Camp beyond the summer with newly president Joan Laporta making it a priority.
[email protected] (Samuel Meade)