The Sunday Mail reports that Abramovich is ready to test Spurs chairman Daniel Levy’s determination to keep the Croatian midfielder at the club.
Levy has previously rejected offers of £22million and £27million for the highly-rated midfielder.
Spurs are reportedly ready to offer Modric a new deal that will see the 25-year-old earn £85,000-per-week, an rise of £20,000-per-week on his current six-year deal with the club.