Solskjaer overlooked a question relating to a recent report that Sanchez could move on and was hardly wholehearted when asked if United would one day see the best of him.
If United make it past Barcelona they face a possible semi-final against Liverpool who, despite Jurgen Klopp's caution, will be expected to brush aside Porto as they did a year ago.
"With Cristiano still in it, I don't think it has opened up all that much", said Solskjaer.
Arsenal inflicted a first league defeat on Solskjaer on Sunday to leapfrog their opponents and leave United two points adrift of fourth spot in the race for a place in next season's Champions League.
After losing 2-0 to Paris Saint-Germain in Manchester, Solskjaer's side claimed a stunning 3-1 second-leg victory in the French capital to progress to the last eight.
It is a prestigious fixture and rich in nostalgia, which will serve up painful reminders of the lost finals of 2009 and 2011 and the lesson at the hands of Hristo Stoichkov and Romario in 1994, along with fonder memories of a Paul Scholes goal to win a semi-final in 2008 and a European Cup-Winners' Cup final in 1991.
"I believe that you get what you deserve in life, in sport", he said. If you put the work in, if you work hard, show the right attitude, if you go in every single day and do the right things you can maximise your chances.
'We want these games against the biggest clubs and the biggest teams.
"The more games you win, the more confidence you breed, the more hunger there is in the players", Solskjaer told a news conference on Friday. "Very disappointed in the result, it hurts more than anything, but it's not like we can't look at the performance and say we were s*** because we weren't". "We're not challenging to win the league this year but we are challenging to win the other two trophies".
"Should both clubs be drawn at home in the same week, the team having finished lower in the domestic league the previous season - in this case Manchester United - will be reversed in accordance with the UEFA Club Competitions Committee principles", a UEFA statement read, per Sky. "(Ander) Herrera's been training, and Jesse (Lingard) training", Solskjaer added.
"The draw is just around the corner for the Champions League and we can't wait to find out who we'll play".