Milan have been drawn away to Shamrock Rovers in the second round of Europa League qualifying, while Tottenham face a long trip to Lokomotiv Plovdiv.
Serie A giants Milan and Jose Mourinho's Spurs are among the big names entering the competition at this stage.
And in Monday's draw, the pick of the ties pitted Milan - who are set to renew Zlatan Ibrahimovic's contract - against Irish outfit Rovers.
Rovers' only previous experience against Italian opposition was in a 3-0 aggregate defeat to Juventus in 2010-11, but they will host seven-time European Cup winners Milan in a one-legged tie.
Tottenham are away in Bulgaria, meanwhile, disrupting the start of their Premier League campaign with the long trip to Plovdiv.
Rangers are also away, visiting Gibraltar's Lincoln Red Imps where rivals Celtic lost in 2016-17, although the Scottish side progressed over two legs on that occasion.
Copenhagen, who reached the quarter-finals in 2019-20 before losing to Manchester United, will make the trip to Goteborg in Sweden.
Wolfsburg, Galatasaray and Basel are each away to Kukesi, Neftci and Osijek respectively.
The ties will be played on September 17, with the qualifying third round draw taking place in advance on September 1.