The deal is set to be a straight swap, after both players passed their medicals on Sunday, with photos of Sanchez in a United shirt already appearing on Twitter.
The English media outlet alleges that both have already arrived at the immigration office in Liverpool to go through the procedure of tying up formalities, with no compliactions expected.
Sanchez and Mkhitaryan have had to apply for an extension on their existing permits, with both players reportedly satisfying the necessary criteria for another three more years under a UK Tier 2 (Sportsperson) visa.
United and Arsenal are expected to get clearance for their new stars straight away but could officially announce the deal sooner-rather-than-later 'subject to obtaining a work permit'.
Mkhitaryan would be cup-tied for the 'Gunners' Carabao Cup semi-final second leg against Chelsea on Wednesday.
However, Sanchez could feature in Jose Mourinho's squad for their FA Cup fourth-round clash with Yeovil Town on Friday night, if the deal is finalised and he is registered as a United player before 12pm on Friday.