Both have been named as seeded teams ahead of the draw. Valencia, Bayer Leverkusen, Shakhtar Donetsk and Sporting Lisbon are among the other seeded sides.
United – making their return to Europe’s elite competition after a year away – could meet either Club Brugge, CSKA Moscow, Lazio, Monaco or Rapid Vienna.
Though United will be heavily favoured to navigate their way through the two-legged tie and book a place in the group stage, assistant boss Ryan Giggs is taking nothing for granted.
“There are no mugs in it at this stage,” Giggs said. “It will be difficult for us to qualify, especially with the play-off being early on in the season, but we are ready.
“We are used to being in the Champions League. It wasn’t nice last year watching your rivals play in it.”
Celtic, bidding to reach the group stage of the competition for the first time since 2013, will face either Maccabi Tel Aviv, Partizan, Malmo, KF Skenderbeu or FC Astana.
Midfielder Nir Bitton helped Celtic defeat Qarabag of Azerbaijan in the third qualifying round and he insists his side will have to be at their best to earn a place at Europe’s top table.
“We have two more games and we want to make it. It will be difficult, it doesn’t matter who we will meet,” he said.
“We need to play as we did against Qarabag if we are to do it, and I hope we will go to the Champions League.”
The two legs of the play-off tie will take place on 18/19 and 25/26 August; the losers will drop into the Europa League group stages.
The draw is scheduled to start at 11:00 BST, with the Europa League play-off draw to follow at 12:00 BST.
You can follow the draw as it happens in our live blog across our Sky Sports platforms.