Lukaku has enjoyed an impressive season on loan at Everton, scoring his 12th goal of the season in the 3-2 win over Swansea on Saturday.
Tottenham were among a host of Premier League clubs interested in signing the Belgian international last summer, and made a cheeky attempt to do a swap deal that involved Emmanuel Adebayor.
Now Spurs chairman Daniel Levy is expected to return with a serious offer for the in-demand forward when the summer transfer window opens.
Chelsea are set to demand big money for the 20-year-old, who they signed for £17million from Anderlecht in the summer of 2011.
But Jose Mourinho is reportedly ready to cash in on the forward who has spent the last two seasons on loan away from Stamford Bridge, with the Blues looking to sign not one, but two world class strikers in the summer.
Despite concerns as to whether Tim Sherwood will remain in charge next season, Spurs are planning on adding a striker, a midfielder and a defender in the summer, that can make an immediate first team impact.