The alleged incident at the Vitality Stadium took place in stoppage time after Raheem Sterling netted a late winner for the Citizens.
Several City supporters made their way onto the pitch to celebrate with the players, and a Bournemouth steward alleges that he was assaulted by Aguero during the melee that ensued.
According to The Sun, the Argentina international now faces a police probe as a result of the incident.
Aguero took to Twitter on Saturday evening to plead his innocence, however, posting: "Great win today! On this story about their steward, I did not hit anyone, this allegation is false, and the tv pictures prove it. C´mon City."