The Sun says Blues are ready to offer Modric £130,000 a week to defect to Stamford Bridge.
That is almost triple the Croatian's £50,000-a-week White Hart Lane wages.
And the Blues are hoping that their mega-money deal will convince the £15million -rated playmaker to cross the capital.
Chelsea want to add some much-needed flair and creativity to a squad that ended the season empty handed.
A Chelsea insider said: "Not having a manager yet won't slow anything down.
"There's a hitlist of players to sign and Modric is right at the top of it."