Clucas asked to be left out of the Hull squad for their 2-1 Championship defeat to QPR on Saturday as he closes in on a return to the top-flight.
Swansea are believed to be one of the frontrunners for his signature, but reportedly face stiff competition from Burnley, who have had two bids rejected.
"Clucas is preparing to play for another club," Slutsky told reporters after his side's loss to QPR. "I think a deal has been agreed.
"It was his decision not to play, but in the next days, I think a deal will be announced. It is a Premier League club. I think it is a decision made all together but it was his as well."
Swans manager Paul Clement is understood to have funds available to him, especially following the £40m gained from Gylfi Sigurdsson's departure to Everton, and admitted that he needs to add quality to his squad in order to avoid a relegation scrap.
"The moment Gylfi's going you know you need to do that. Without him, [Fernando] Llorente and Ki [Sung-yueng], when they're out, we are weaker," he said.
"We still have a good squad, but we absolutely need more quality players to come in so we have a chance of being competitive this year.
"The situation is very fluid at the moments: texts, emails and telephone calls are going back and forth between various parties. We hope by the deadline - and someone asked me would it be before Crystal Palace [on 26 August] - but as soon as we can do it the better.