Slutsky has been charged with leading relegated Hull back to the Premier League and the Russian is also looking to secure some of Chelsea's players on loan deals.
Hull have yet to begin formal negotiations for Kalas and are expected to face competition from Fulham, who could look to bring back their former loanee on a permanent basis.
He helped Middlesbrough to win promotion to the Premier League during his loan spell in 2015/16 and, last season, was part of the Fulham side which reached the Championship play-offs.
But Kalas is growing increasingly frustrated with life on loan and he is ready to accept a permanent deal away from Stamford Bridge.
The 24-year-old has only one year left on his Chelsea contract and the Blues risk losing him on a free, if they don't sell him in the summer.
No fees have yet been discussed but Chelsea will aim to get back the £5.2 million they spent to sign him from Sigma Olomouc in 2010.