The Russian boss took over from Marco Silva in June after Hull were relegated to the Championship. However, the decision hasn’t yielded positive results so far, as Hull have won just four of 15 league games under Slutsky's command.
In quotes from BBC Sport, Slutsky said: “I think 15 matches is normal time for a decision and if the owner decides about me I will agree, no problem. The biggest pressure is myself. I don't need extra pressure because I always evaluate every situation and I don't satisfy my level now.
“I am my own most serious analyst; I am never saying 'it's not my fault'. I will agree with the owner's decision in this situation. If he lets me continue to work I will try to change the situation.
While, Hull currently sit in 17th place in the Championship table, they are only seven points off the playoff spots.
Slutsky, a former goalkeeper, became the first Russian to manage professionally in England, when he took over at the Tigers in the summer. He has had previous success with CSKA Moscow where he won three Russian Premier League titles.