If four British men qualify to play singles, it potentially becomes more straightforward.
World number five Joe Salisbury and 10th-ranked Neal Skupski could complete the maximum six-man team: Skupski to play with Evans, with whom he has enjoyed previous success, and Salisbury with Murray, having only been denied a semi-final place in Tokyo by a brilliant Croatian comeback from Marin Cilic and Ivan Dodig.
But if Evans does not make the team, it becomes trickier, especially as Salisbury and Skupski are open about the fact they would prefer to play together.
“We definitely enjoy playing together and think we can do well. I think that would be the number one choice for both of us,” Salisbury told BBC Sport at the Madrid Open.
“I’ve always loved playing with Joe,” Skupski added.
“Every time I get on court with Joe, it’s real special and hopefully we can play the Olympics together. We are just waiting to see what the guys at the LTA think.”
Only top-10 players are guaranteed a place in the draw, and so Skupski may have to match last year’s run to the French Open quarter-finals to make sure of that position.
Entry is otherwise determined by a pair’s combined ranking, which is calculated by adding their singles or doubles ranking together.
If Murray says he would like to play both singles and doubles, it would be a brave call to deny him the opportunity in what is expected to be the final tournament of a glittering career.
Medals are also on offer in the mixed doubles, which allows no more than one pair per country. The entry list will be drawn up from the rankings in the week before the Games, with places only available to previously selected players. As things stand, Salisbury and Boulter would have the strongest chance of earning a place in the draw, but Boulter may not feel able to play in all three events.