The Red Devils are supposedly in the market for a centre-back to partner Harry Maguire from next season and are big fans of the Slovakia international.
Manchester City are also believed to be in for Skriniar, but United are said to have made the first move for the 25-year-old by stepping forward with an offer.
As the speculation over Skriniar's future continues to rumble on, Sports Mole looks at the shirt numbers available to him should he make the switch to Old Trafford.
Skriniar has spent the past three seasons with Inter and has worn the number 37 shirt in each of those, though that number is currently occupied at United by academy graduate James Garner.
At first club Zilina, meanwhile, the defender was in possession of '3' - traditionally given to left-backs - which is held by Eric Bailly at Old Trafford.
The Slovakian also plays with the number 14 on his back for his national side, as he has done since 2016, and that could become available at United this summer.
Marcos Rojo has had that shirt since 2018 but has spent the last seven months on loan with Estudiantes and is unlikely to return.
In terms of other possible options for Skriniar, '4' may also soon be freed up as long-serving Phil Jones has been tipped to join a new club at the end of the campaign.
'Seven' is another that is up for grabs if Alexis Sanchez leaves permanently, though that is of course more associated with attacking players.
The number 12 shirt is arguably the next-best choice for Skriniar, with that number belonging to Chris Smalling before he headed to Roma on loan.