Saul failed to nail down a regular spot in the La Liga champions' starting lineup last term - starting 22 of their 38 top-flight matches - and Atletico are thought to be open to a summer sale for the right price.
Meanwhile, Silva played a key role in Man City's run to the Champions League final last term, but he too struggled for consistent starts in league action and is reportedly on the Citizens' transfer list.
According to The Times, Silva is indeed keen to end his stint at the Etihad this summer, and Atletico are interested in a move for the former Monaco midfielder.
The report adds that a swap deal involving Saul is a realistic possibility, but Manchester United, Bayern Munich, Liverpool and Chelsea are all rumoured to be keeping tabs on the Spaniard's future as well.
The two midfielders still have several years left to run on their respective deals, though, as Silva's contract at City runs out in 2025 while Saul is not due to become a free agent until 2026. body check tags ::