Defending champion Djokovic faces Thompson on Wednesday, and though the odds will be heavily stacked in the Serbian's favour, his 70th-ranked opponent has an ace up his sleeve, having consulted with Kyrgios ahead of the second-round clash.
Kyrgios, who pulled out of Wimbledon with a wrist injury, is part of an exclusive club of tennis players with a superior head-to-head record against Djokovic, with the Australian's sole defeat to the world number two coming in last year's final at the All England Club.
"Nick's beaten him a couple of times," Thompson told reporters on Monday.
"He played him in the final and it wasn't an easy match. As much as everyone thinks that Nick doesn't have care in the game, he has a big tennis brain, so it'd be silly of me if I didn't try to pick it...
"I know the odds are firmly against me. But yeah, just get out and enjoy it and just have fun. It's not every day you play Novak at Wimbledon. It could be a dream, or could be a nightmare."
RAIN PLAYS SPOILSPORT
The first two days of the tournament have been significantly affected by rain, which caused matches on outside courts to be suspended or cancelled on Tuesday.
The cancellations have caused a scheduling headache, adding to an already long list of matches that had been carried over from Monday.
Tunisian sixth seed Ons Jabeur, who was among the handful of players to complete a match on Tuesday, told reporters she felt lucky to play on Court One, adding: "It's a shame that the weather is like this. Hopefully it will get better the next few days."
The outlook for Wednesday appears promising, however, with Britain's Met Office predicting a low chance of rain throughout the day, which could enable organisers to begin wading through the sizeable backlog.
The jam-packed men's schedule for the third day of the Championships features a host of high-profile names in second-round action - including top-10 seeds Casper Ruud, Andrey Rublev and Jannik Sinner, as well as three-time Grand Slam champion Stan Wawrinka.
Third seed Daniil Medvedev and fifth seed Stefanos Tsitsipas will also complete their postponed first-round matches.
In the second round of the women's draw, world number one and French Open champion Iga Swiatek takes on Spaniard Sara Sorribes Tormo, while twice major winner Victoria Azarenka and French fifth seed Caroline Garcia are also in action.
Women's top-10 seeds Maria Sakkari, Petra Kvitova and Barbora Krejcikova will play their opening matches of the tournament.
