Hull City boss Leonid Slutsky is wanted at Chelsea to replace Michael Emenalo.
Emenalo has resigned as technical director after ten years with the club.
Abramovich could turn to Slutsky to replace Emenalo. However, Chelsea director Marina Granovskaia is in line to fill the post, according some sources.
Meanwhile, Slutsky's agent Sandro Varga insists he won't walk away from the Tigers.
He told sports.ru: "The question of the resignation of Slutsky from Hull is not even considered. Fans continue to support him.
"The club management understands all the circumstances that now do not allow Slutsky to achieve results, so the question of the resignation of the coach is not even considered. Slutsky will be Hull at least until the end of the season.
"With the fans of Hull Leonid does not have any problems. I was at one of the last home games of the team - the fans continue to support him.
“In the locker room and at the training ground there is a great atmosphere. I think he should continue to bend his line and the results will come."