The Sky Sports pundit, who specialises in Spanish football, says the club approached the Real Madrid midfielder a 'few weeks ago' with the response that he was 100 per cent staying at the Bernabeu.
However, Alonso has since reportedly agreed terms with Bayern Munich and looks set to join up with former Barcelona boss Pep Guardiola - as well as ex-Liverpool team-mate Pepe Reina.
Man United have signed Ander Herrera for £28.8 million this summer but still look short of midfield reinforcements.
XA decission 2 leave Madrid took club by surprise. MUFC approached him few weeks ago and agent and club answered, He's 100% staying.— Guillem Balague (@GuillemBalague) August 28, 2014
United will likely be disappointed that Alonso has opted to join the German champions if the story of their enquiry is true.
The 32-year-old yesterday announced his official retirement from international football, prompting a flood of tributes from footballers past and present.
His passing style will likely suit Guardiola's tactics, while Madrid's signing of Toni Kroos the other way may fill the void left by the Spaniard at the Bernabeu.
Manchester United, meanwhile, travel to Burnley on Saturday and have at least completed the signing of one Real Madrid player - Angel Di Maria - this week.