Andy Murray, Dan Evans and Jack Draper have been drawn in the same section as top seed Carlos Alcaraz for Indian Wells.
Evans will join the tournament in the second round, since he is among the top-32 seeds, and could face Draper in his first match.
The winner of that would play Murray, if the three-time Grand Slam champion beats Tomas Martin Etcheverry and Pablo Carreno Busta.
It guarantees two Brits will be out before the fourth round where US Open champion Alcaraz will likely await one of Murray, Evans or Draper.
Alcaraz is in line to face defending champion Taylor Fritz, Jannik Sinner or Holger Rune in the semi-finals.
Having recently won three titles in three weeks, Daniil Medvedev is the favourite to win the first Masters event of the season.
Medvedev will play either Brandon Nakashima or John Isner in his first match, with a potential quarter-final against Casper Ruud.
Cameron Norrie could have a tricky opener versus Alexander Bublik, with Matteo Berrettini next in the last 32.
Should Norrie go deep into the tournament, matches against Andrey Rublev and Stefanos Tsitsipas are possible just to reach the semi-finals, where he might find an in-form Medvedev.
World No. 1 Novak Djokovic withdrew from the tournament on Monday due to his vaccination status and Rafael Nadal is recovering from an injury he sustained at the Australian Open.
RADUCANU COULD FACE SWIATEK IN LAST 32
Iga Swiatek will start her title defence against Alison van Uytvanck or Clarie Liu, with a potential clash against Emma Raducnau further down the line in round four.
Raducanu plays Danka Kovinic in the first round on Wednesday, with the winner taking on Poland’s Magda Linette.
Former Grand Slam champions Sloane Stephens and Sofia Kenin have drawn each other in the first round, as Elena Rybakina awaits the winner of the all-American clash.
Coco Gauff and Olympic champion Belinda Bencic are set to meet in the fourth round, with newly-crowned Australian Open winner Aryna Sabalenka a potential match-up for one of the players in the quarter-finals.
Britain’s Katie Swan and Katie Boulter need to win one more qualifying match on Tuesday night to reach the main draw.