Hull are allegedly keen to make a final decision as soon as possible and it has been claimed that an announcement could be made in the next 24 hours.
Chelsea are looking for a new technical director after Michael Emenalo ended the best part of a decade working at Stamford Bridge by leaving the club last month.
The defending champions are yet to decide whether Emenalo, who is now at Monaco, should be directly replaced by Slutsky or whether the role should be shared between the two.
However, his time at the club was short lived after winning just four matches in the Championship, which has left the club in 20th place on the table.
Slutsky was granted access to Chelsea games last season and visited the club's Cobham training ground.
Taylor Swift Turned to Kesha for Advice During Groping Case
In that moment, I made a decision to forego any courtroom formalities and just answer the questions the way it happened". He was sacked from country radio station KYGO days after Swift's management team reported what happened.
Slutsky said: "I would like to really thank everyone associated with Hull City from the players and staff to the owner and especially the fans".
Hull now sit 20th in the Championship table, and are without a win in five games, recently drawing 2-2 with Sheffield Wednesday on Saturday.
The club confirmed Slutsky's departure in a statement and also said head of club strategy Oleg Yarovinsky had left his role at the KCOM Stadium.
"I am very proud to have been through this experience, it was challenging but a very exciting time for me".
- Young & CO. LTD. Boosts Holdings in Air Products & Chemicals, Inc. (APD)
- Ryan Reynolds To Do Some Pokemon Sleuthing In 'Detective Pikachu'
- RBI caps MDR to boost debit card transactions
- Assassin's Creed Rogue HD rated for current-gen consoles in Korea
- Lamborghini Working On Plug In Hybrid Lamborghini Urus SUV
- $3.92 EPS Expected for Broadcom Limited (AVGO)
- Prince William and Kate Middleton at the Children's Global Media Summit
- Two Killed in Gas Pipeline Explosion in Lee County Identified
- Singapore Airlines Changes Flight Routes Over N.Korean Missiles
- 'Baby Driver' Director Edgar Wright Comments On Kevin Spacey Allegations