Walker is said to have consulted Riyad Mahrez, who left Manchester City for Al Ahli this summer, about life in Saudi Arabia.
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Recently, there were also rumours of a new attempt from Bayern Munich - which failed to bring about a transfer last year.
This season, Walker has made four assists in 28 appearances, including 27 starts, in the Premier League.
The right-back's contract with City runs until the summer of 2026.