Jose Mourinho admitted the diagnosis does not look good for Zlatan Ibrahimovic and Marcos Rojo, after they were forced off with injuries in Manchester United's Europa League quarter-final win over Anderlecht.
Rojo's injury leaves United potentially short in defence as Phil Jones and Chris Smalling are sidelined.
"I don't want to go in that direction", he said when asked about the championships in Poland.
Marcus Rashford scored United's extra-time victor against Anderlecht and looks set to deputise up front for top scorer Ibrahimovic, who is still to commit himself to United beyond the end of the season.
United's record goalscorer Wayne Rooney made his return against Anderlecht, taking his place on the bench after missing four games with an ankle injury, but Mourinho suggested the club captain is not yet ready to play.
When it was put to him that he was facing a significant lack of options at centre-back, Mourinho mentioned Daley Blind - Rojo's replacement from the bench - before suggesting Jones and Smalling needed to be "brave".More news: Democratic Party rides coattails of Bernie Sanders' popularity
"I just feel that when a player reaches a certain level, it doesn't make a lot of sense to drop levels", he said.
And I think it's time for Jones and Smalling to be fearless, to risk.
Henrikh Mkhitaryan's 10th minute opener, assisted by Rashford, gave United the lead their had deserved for their early dominance. "Miracles I don't expect - but you have to try to do everything to accelerate the process".
Mourinho, meanwhile, said the 19-year-old Rashford "cannot play every game".
Manchester United switch their focus back to the Premier League as they travel to Burnley on Sunday (14:15 BST) before travelling to Manchester City on 27 April (20:00). "So instead of coming mid-May you can come the beginning of May, this kind of acceleration of the process".
"I'd love to see them both", he added.