There are plenty of great options: Giggs, Scholes, Baresi, Maldini, Facchetti, Puyol, etc.
For me though, the greatest is Francesco Totti. The others above played for clubs who won multiple trophies, and all won the champions league at least once. Aside from a smattering of Coppa Italias and one Scudetto, Totti didn’t win anything with Rome.
For me, it’s easier for a top player to stay at a top club, rather than be a top player like Totti and stay at a club that was rarely considered the best in Serie A. For my money, he is the greatest one-club man of all time.
Who would you choose?
Don’t agree with people mentioning Müller, Maldini, etc. Great players and most definitely legends of their clubs but it’s Bayern and AC Milan - they won everything there and always had the opportunity to win everything there. It’s not like it’s difficult to stay.
For me it’s Ledley King. Turned down Madrid and Barcelona interest as a teenager, stepped up for Spurs during one of the darkest days at the club (Judas…), is currently a club ambassador, and continues being involved in community outreach in Tottenham and beyond. One of the best defenders in the PL at his time despite having virtually no cartilage in his knees. The man didn’t train and still played on the weekends and was frequently the best player on the pitch. Absolute superhero. I can only wonder what heights he would’ve reached had he not struggled with his injuries.