According to reports, the 26-year-old Barcelona midfielder has told friends in English football he wants to end his two-year stint in Catalonia.
Fàbregas, who is concerned about his lack of game time for club and country, would be a regular starter at United, whose midfield shortcomings have been memorably exposed in recent seasons.
The former Arsenal captain started 38 games for Barça last season but has failed to break the club's immovable triumvirate of Xavi, Andrés Iniesta and Sergio Busquets.
Competition for midfield berths in Vicente del Bosque's Spain squad ahead of the 2014 World Cup is fierce. Real Madrid's Xabi Alonso was dropped for the Confederations Cup and Fàbregas, who didn't complete a full match in Brazil, did not feature in either La Roja's semi-final win against Italy or final defeat to Brazil.
United have had £26 million and £30m bids for Fàbregas rejected by Barça, who appointed Gerardo Martino as their new coach this week.
The Red Devils' executive vice chairman Ed Woodward returned home earlier than scheduled last week to attend "urgent" transfer business.
Fàbregas is yet to link up with his Blaugrana teammates after he was granted an extended break following the Confederations Cup.