Slutsky, 46, became the first Russian manager to work in the Football League when appointed as Marco Silva’s replacement earlier this month.
Silva’s initial success after succeeding predecessor Mike Phelan in January led to the return of stay-away fans, who have protested against the Allam family’s running of the club since their failed attempt to rebrand as Hull Tigers in 2013.
When asked about the fractured owner-fan relationship, former CSKA Moscow and Russia head coach Slutsky told ESPN FC: “It’s not the first time!
“And if I can help to get back the relationship between the club and the supporters I will be very happy.
“I never listen about other situations. I don’t know the owners’ plans, but I think that the family does a lot of things in Hull, really serious investment in the city, and I hope the situation with Hull City will be stability.”
Hull have yet to make their first summer signing under Slutsky, while fans are braced for more player departures following the sales of defenders Curtis Davies and Harry Maguire.
“Yes, of course we need some players, but it’s like in every club,” Slutsky added.
“There are players you want, who don’t want to play in this city. There are players who want to play in this city, that maybe you don’t want.
“But we have a strategy about new players, about loan players and in the last two weeks I am working hard with players and having a lot of conversations with agents.
“It’s not a quick process, but I hope we will have some new players before our trip to Portugal on July 11.”