The 23-year-old Argentine was named the best defender of the latest Eredivisie season after his strong performances.
And Atalanta would like him to replace another former San Lorenzo defender José Luis Palomino.
Meanwhile, Sevilla were keen on Senesi when he played for San Lorenzo, offering €4m in the summer of 2017.
Three years later and Sevilla have submitted an offer of €15m plus €2m in bonuses. Their La Liga rivals Getafe also made a similar proposal.
But they will have to do better with Feyenoord rejecting those bids and demanding at least €20m.
The Dutch side have told his father Riccardo, who takes care of his interests, that they would like to keep him next season.
Since his arrival in Rotterdam, Senesi has made 25 appearances in all competitions, scoring three goals.