The Argentina international, who is currently recovering from injury, has been linked with a move to Spain but his father says there is "nothing at all" in the rumours
The Argentina international has been in superb form for his club this season, scoring 19 times in all competitions, though is currently sidelined with a calf injury.
The 25-year-old's goalscoring exploits in the Premier League have seen him linked with a return to La Liga, but his father insists there is no interest from Barcelona.
Asked about Aguero being linked with a move to Camp Nou he told Mundo Deportivo: "I would like to see Sergio and Messi playing together but there is nothing at all."
City will face the Spanish champions in February after being drawn together in the Champions League, a match Aguero senior is looking forward to.
"Sergio and Leo always speak and more after the Champions League draw," he added.
"They're good friends, like laughing and they're already joking between them ahead of the City v Barca clash.
"We will see two great games. I don't know if I will visit Messi's home, but I will go to the hotel for sure to say hello to him."
Aguero's father is also confident Manuel Pellegrini's side can knock Barca out of the competition and has warned Gerardo Martino's outfit to be wary of the Premier League side.
"I think it will be a 2-0 in England and at least a 0-1 in Barcelona," he added. "I love Messi so much, but I want my son's team to win. It's a pity both Barca and City are facing each other so soon.
"I wish Sergio to score but the main thing is Manchester City win. Barca's players are all great but they should be careful of City's ones, as they are very good as well.
"They are hungry and they need to rule Barcelona out of the Champions League if they want to keep winning titles."