Manchester City have brought in Jack Grealish this summer at a cost of £100m and are prepared to move several players on if the opportunity arises.
Bernardo has been heavily linked with an exit from the Etihad Stadium and he is keen to move on.
The Portuguese midfielder is continuing to push to leave Manchester City, according to Italian broadcaster Sportitalia.
The player’s agent Jorge Mendes is working to find a solution, while he also works on taking another one of his clients to Manchester City.
Mendes is negotiating a move to Manchester City for Cristiano Ronaldo.
Bernardo joined Manchester City in the summer of 2017 from Monaco and after winning three Premier League titles at the club is keen for a new challenge.
The 27-year-old has another four years to run on his Manchester City contract.