Benfica are looking to appoint a successor to Jose Mourinho, who has left the club and signed a three-year deal to become Real Madrid’s new head coach.
Mourinho, 63, took over at Benfica for a second spell in September and led them to third place in the Primeira Liga.
Silva joined Fulham in July 2021 from Everton and guided them back to the Premier League in his first season, following the club’s relegation to the Championship a year earlier.
The Cottagers finished 11th in the top flight last season, level on 52 points with Chelsea.