The Egyptian and Swiss pair have been attracting much Premier League attention of late after impressing for their club side both domestically and in Europe.
Liverpool and Tottenham have been linked with Salah, while Arsenal are rumoured to be watching Schar.
But United are ready to beat their domestic rivals to both players with a joint £30m offer.
Despite claims that he is not willing to panic buy in January, David Moyes is believed to be open to securing new names to bolster his squad and attempt to right the wrongs of a woeful opening period of the season.
A lack of creativity in the final third is said to be worrying the Scot, who may look to address the issue with a move for Salah.
The 21-year-old has been earning rave reviews for his displays of late, and even netted two vital goals against Chelsea in the Champions League this season.
Schar is also on Moyes’ radar, with eventual replacements for Rio Ferdinand and Nemanja Vidic needed.
The five-time Swiss international is set to feature at next summer’s World Cup and has become a regular starter at Basel in recent times.