The Japan international has played 18 times this term but they have only started six games across all competitions.
Despite this, according to PA News Agency, Liverpool have turned down both of these approaches.
While Minamino is well behind Mohamed Salah, Sadio Mane, Roberto Firmino and Diogo Jota in the pecking order Jurgen Klopp’s side are still in four competitions – they have a League Cup final against Chelsea in a month’s time – is it believed there is no real desire to offload the 27-year-old.
It would take a considerable offer for them to be persuaded to consider allowing the player, signed from RB Salzburg in January 2020 for £7.25million, to leave.
Atalanta are also understood to be considering striker Divock Origi as a serious option should their Newcastle-linked Colombia international Duvan Zapata move to the Premier League.