If Slutsky has been living in England since January, and realized his possible options for getting a job were likely only to be one of the lower 5 or 6 teams at the bottom end of the PL at the turn of the year, it is highly probable he has been focussed on watching those teams with interest for that period. He would, if shrewd, have done his assessment of the potential of each of those teams from two aspects.
a) If relegated, what would be needed to get them up from the Championship next season
b) If just missing relegation, finishing 15th, 16th or 17th, what would be necessary to improved their final position in the PL the following season.
5 months of analyzing ( videos and/or attending live games) player strengths, weakness, ownership styles & ambitions, financial backing etc and stability.
He may be very well prepared for impressing in interviews with any of those 5 or 6 teams by now. If his friendship with Abramovitch is as close as the press suggests, he (A) is likely to have given him plenty of advice, directly or through his contacts. Abramovitch may not want to see his "buddy" fail in his first foray into English football- and may well advise him to gain some experience in the Championship first, and give him some support in that role where there would be the least conflict of interest - namely a different division to start with.
Observation of Silva's efforts at City since his arrival may well give him o strong indication of what he could possibly achieve at the KCom !