The first leg tie against Ligue 1 outfit Saint-Etienne is our 40th of the campaign, with the possibility of a 65-match season with a run to the Europa and FA Cup finals.
Jose said: "It is a really complicated situation but we cannot choose competitions at Manchester United - the Europa League is on a Thursday which makes it even more difficult and at least one match will be postponed also.
"If we progress in the FA Cup and in Europe, we will be in trouble in April and May.
"But we play to win every game so this is a problem we have to contend with.
"There are a lot of doors open - we are in the last 32 but not eight or four so there is a long way to go.
"They (Saint-Etienne) are a French club with a lot of history and success, like Manchester United and they have won the most titles in their country so it's a big club with a big tradition."
"Le Verts" arrive at Old Trafford amid another quietly impressive campaign, sitting in fifth place in France (albeit 19 points off the top) having topped their Europa League group with an unbeaten record (three wins and three draws).
Marcos Rojo is fit to face Saint-Etienne at Old Trafford, but Phil Jones, Michael Carrick and Wayne Rooney are all sidelined due to "minor issues".
An intriguing sub-plot to the tie sees Florentin Pogba, elder brother of Paul, line up opposite his sibling at the heart of the defence for Christophe Gaultier's side.
The third Pogba brother, Mathias, is also a professional player with Sparta Rotterdam in the Eredivisie.
United have won 13 of their 26 meetings against sides from across the channel, with 11 draws and only two defeats.
The last of those encounters came in 2011 as United edged out Marseille 2-1 at home to move into the Champions League last eight.
This meeting marks the first of four cup contests in a row, with Blackburn away in the FA Cup on Sunday, then the return in France before the EFL Cup final with Southampton at Wembley.
Form guide: United D L W D W W Saint-Etienne W W L W L W
Match odds: United 1/3 Draw 4/1 Saint-Etienne 10/1
Referee: Pavel Kralovec (Czech Republic)