Slutsky targeted the 29-yer-old immediately after his appointment by Hull last week as he is keen to reunite with Doumbia who played under him for five years at CSKA Moscow where he scored 61 goals in 95 appearances.
He joined Roma on a four-and-a-half-year deal in January 2015 from the Russian side for a fee of £11.5 million but failed to make the same impact in the Italian capital.
ClubCall reports that Doumbia is understood to have rejected the chance to join the Tigers in a £3.5 million deal from Roma.
Giallorossi reported that the player does not want to move to the Championship and another report on 72.co.uk, suggested that Doumbia is not keen on returning to England after his poor spell at St James Park with Newcastle United in 2016 where he only made three appearances for the Magpies.
Roma had loaned Doumbia to Swiss champions FC Basel where he scored 21 goals in 35 appearances last season. He also scored twice for The Elephants in their 3-2 loss over Guniea in a 2019 Africa Cup of Nations Qualifier on Sunday.