The Burly Belgian striker is currently on loan at Everton and has widely been tipped to return to Stamford Bridge at the end of the season after impressing for the Toffees.
However, it is believed that Jose Mourinho is not the youngster’s biggest fan leading to talk that he is ready to cut him loose if a swoop for Costa can be sealed.
The Spanish international is seen as a top target for the Blues, with ‘The Special One’ ready to sanction a £31.5m spend to land the goal-getter his side have been missing this term.
Even with the futures of Samuel Eto’o. Fernando Torres and Demba Ba far from clear, Lukaku may also lose out if Costa is snapped up.
Spurs are one of many sides said to be keen on the 20-year-old, and are believed to be ready to meet Chelsea’s £20m valuation.
Everton themselves may also enter the battle, but much depends on their ability to qualify for the Champions League.
Lukaku rose to prominence during a loan stint with West Brom last term, and has continued to impress during the current campaign on Merseyside.