Mourinho, sacked by Chelsea earlier this term, believes he will get the job despite possible public employment tribunal involving Eva Carneiro, who has a personal legal action against him for alleged victimisation and discrimination.
Senior figures on the Man United board, however, would like Giggs to take over from Louis van Gaal.
It is a precarious situation for the club as they risk upsetting Giggs, a United legend, if they overlook him in favour of Mourinho.
However, following what has been a turbulent period under van Gaal, United need proven experience to take them back to the top.
Mourinho has that in abundance, having won trophies at every club he has managed. Giggs, although a romantic option, is hugely inexperienced and it would be a gamble taking him on.