Manchester United executive vice-chairman Ed Woodward hopes David De Gea and Marcus Rashford will sign extensions by May.
Woodward has recently tied Phil Jones, Chris Smalling, Ashley Young, Anthony Martial and Scott McTominay to new deals.
Locking down De Gea and Rashford would prove to be another coup, and Woodward remains hopeful.
In a conference call with journalists, Woodward said United are "hoping to finish off the final few" contract renewals before the end of the season.
Ander Herrera and Juan Mata are also out of contract at the end of the season.