Pep Guardiola says Manchester City have "a lot of business to do" this summer, but did not entertain questions about Arsenal's Alexis Sanchez.
Kompany has missed large chunks of the season due to injury.
Pep Guardiola's side enjoyed their first win in five Premier League matches last weekend, a straightforward 3-1 home victory over struggling Hull making City a little more secure in fourth place.
Guardiola also insisted that City captain Vincent Kompany could have a role to play at the club heading into next season. He can do that. "After Chelsea he reacted and had problems in the leg and we didn't want to take risks".
When asked about the reports, Guardiola replied: "Now is not the time to talk about that. From what I have seen in the last few days he is ready for the next game".
Claudio Bravo was the undisputed number one goalie for the Citizens, but has lost that spot to Caballero after a string of poor displays.
The latter's concession rate is far superior, too, at 0.82 goals per game to Bravo's 1.30 - and the Chile global is also lagging behind in saves and catches.
As reported by City's official website, Guardiola said: "Last week I decided on Claudio, and Saturday I will decide [again]".
"In the training session we involve both so we are going to see".
"Of course we follow all the players who are on loan and of course we are following Joe every weekend".
Bravo's arrival in the summer prompted the departure of England global on Joe Hart on a season-long loan to Torino.
"I want both goalkeepers to be involved - I have confidence in both of them", he said.
"But we're in a world where we don't know where we'll end up".
"I was really impressed when they came here [in October, in a 1-1 draw] in what was a busy time for us".