The Villans are sitting seventh in the Premier League table and are eyeing securing European football on the final day of the season.
Unai Emery has turned them from potential relegation contenders to the dreaming of the prospect of playing European football since arriving earlier in the season.
Villa are keen to back him in the transfer market in the summer and the Spaniard wants to add more attacking threats to his squad.
And it has been claimed that Martial and Lukaku are two strikers the Villans are closely monitoring.
The Frenchman has had another injury-troubled season and Manchester United are prepared to sell him in the summer.
Lukaku has been on loan at Inter this term and is keen to continue playing in Italy.
But for the moment, it seems unlikely Inter will be prepared to take on his massive wages for one more season on loan.
There is also no clarity on whether the Belgian will have a future at Chelsea under Mauricio Pochettino.
Aston Villa have their eyes on the duo with a view to potentially signing one of them in the next transfer window.