Anderson acknowledges that the pull of family in his homeland of Portugal had become impossible to resist after nine years in England.
Andersen joined Fulham from Crystal Palace in the summer of 2024 and credits Silva with having a profound influence on his development as a player and his understanding of how football at the highest level should be played.
"Marco has taught me incredibly much about the game. He is a manager who wants to play football. And his very good footballing philosophy appeals to me."
He was equally expansive about Silva's legacy at the club.
"Marco has meant incredibly much to Fulham. He has achieved some of the best results in the club's history.
"That is why he is loved by the club's fans. Last season, Fulham achieved the best results in the club's history. This season, we were close to beating that. We were also close to qualifying for Europe."
On Silva's reasons for leaving, Andersen was understanding and without resentment.
"It's a difficult situation for him, because his entire family lives in Portugal. He has now been nine years in England, so of course it plays a role when the family is at home in Portugal."
Silva is widely expected to take over at Benfica, replacing José Mourinho who has departed for Real Madrid. Andersen on Wednesday played his 50th international match for Denmark, with the national side preparing to face Ukraine in Odense on Sunday in front of a near sell-out crowd of 14,000.