Lukaku is on the verge of sealing a return to Stamford Bridge, with the Blues reportedly paying £97million for his services.
And the Sun reports that Inter will turn to Lukaku's former Manchester United teammate in Martial to step in for him.
It's understood the Italian champions want to sign Martial on a season-long loan but Man United would prefer a permanent deal. However, the Red Devils would agree to the loan option if it included a commitment to buy next summer.
The two clubs have done business in the past with Man United previously letting Ashley Young and Alexis Sanchez go to the San Siro.
Martial, reported to be on £200,000 a week, has three years left on his Old Trafford contract, plus a 12-month option.
The 25-year-old's place in the team is far from guaranteed, even before the knee ligament injury which ended his season in March.
Edinson Cavani is their main goalscorer while Mason Greenwood, Marcus Rashford and new signing Jadon Sancho are all ahead of Martial in the pecking order.
Martial joined United from Monaco in 2015, and made an immediate impact with a goal on his debut against Liverpool.
But his Man United career has been stop-start over the past couple of years. He managed just four goals in 17 Premier League starts last term.
Speaking after Saturday's 4-0 friendly win over Everton, boss Ole Gunnar Solskjaer admitted: "Anthony has had a bad spell with injuries.
"He's been training well with us but as players who've been out for a while, they need some more sharpness, need some more work.
"He tried to do the right thing; it didn't come off all the time, but it's better than what you fear sometimes when he's been injured for five months - since March."