Manchester City's all-time record goalscorer left his boyhood club for Atletico Madrid 14 years ago and has frequently spoken of a desire to end his career with El Rojo.
Aguero is 32 in June and contracted to City until 2021, while the appointment of his former team-mate Pusineri as Independiente boss earlier this year has reignited talk of an emotional homecoming.
"Hopefully it will be my turn to be the coach of Kun Aguero," he told Super Miter Deportivo. "I was a team-mate of his and hope that in the future I will get to be his coach.
"Hopefully in my stay at Independiente, I can come to [reunite with] Sergio. We are keeping him the number 10."
Pusineri revealed he is in regular contact with the Argentina striker, although he denied forcing the issue of an Independiente return.
"In recent days I did not speak to him," he said. "We spoke two months or so ago, when I congratulated him on a good week he had had with many goals.
"It will depend on the desire or will that he puts on his return, that is why I say that one is excited to [prospectively] see Sergio again at Independiente, continuing to give joy to the people of Independiente."
Independiente won the last of their seven Copas Libertadores in 1984 and Pusineri believes trying to bring long-awaited continental glory to the club would certainly appeal to Aguero.
"To have Sergio again would be wonderful for all of us who love Independiente," he added. "If I put Independiente in the Copa Libertadores, it would be an important challenge to play with Aguero and for all the people who love him.
"People love him and he is an idol. Hopefully if we manage to be competitive on a slightly higher level, [we will] also be able to count on his help."
Aguero has 254 goals in 368 games for City, with 180 in the Premier League placing him fourth in the all-time standings in England's top flight, where he has also scored a competition-best 12 hat-tricks.
Independiente finished a disappointing 2019-20 Argentine Primera Division season in 14th position.