The Gers travel to Dens Park to face rock-bottom Dundee, who have won just two of their 14 Scottish Premiership outings this season in what will be interim boss Graeme Murty's fourth match in charge since Pedro Caixinha was sacked.
Rangers suffered an abysmal 2-0 defeat to Hamilton at home last time out, and will be looking to put that right this time around with the odds stacked in their favour as their away form continues to be a rare shining light amid their darkness.
Thompson claimed the Gers will beat McCann's side away from home, and also stated that he expects out-of-form striker Alfredo Morelos to be dropped, after the 21-year-old has failed to score in his last nine games.
"Their home record has been so, so bad, just six wins in 2017 but their away record is the opposite," Thompson said. "I think that is down to the Rangers players not doing well in front of the 50,000 home fans with that weight of expectation on their shoulders.
"I do think Rangers will win, as they've scored 10 goals in their last three away games. They enjoy playing away, but this is on the back of a really minging performance against Hamilton. He's hinted at dropping Morelos; he's bereft of confidence.
"I think he may get dropped. But I'll for a Rangers win, they have enough quality to do the job if everyone pulls together."
Three points and a third win in four games for Murty's side will see them climb into second place in the Scottish Premiership table, with Aberdeen and Hibernian playing this weekend.
Murty will be hoping his side can produce a repeat of the fixture at Ibrox earlier in the season, which saw Rangers strol past Dundee with a 4-1 win thanks to goals from Josh Windass, Carlos Pena and a brace from Alfredo Morelos.