The La Liga club, who beat Barcelona 2-0 in the first-leg of their Copa del Rey quarterfinal on Wednesday, want to add Martial to their squad to boost Champions League qualification hopes.
A move for Morata failed this week and the Spain international is set to join Atletico Madrid, with Sevilla unwilling to pay his €10 million salary and loan fee.
Sevilla have a long-standing interest in Martial, and sources have told ESPN FC that they are ready to test United's determination to hold onto the France forward.
Martial is in discussions with United over a new contract to replace his existing deal, which expires at the end of next season.
The 23-year-old had been considering his future at Old Trafford due to a difficult relationship with former manager Jose Mourinho, but has become a regular under caretaker Ole Gunnar Solskjaer.
Sources have told ESPN FC that Martial is now much happier and is ready to commit to a new contract, but Sevilla are prepared to explore the possibilities of signing him this month if United offer any encouragement.