LEAGUE One and League Two clubs will vote next month on whether to revise the format of the Checkatrade Trophy or scrap it entirely.
Some academy teams were allowed to play in the tournament for this season only, with Saints taking up the invitation and enjoying a run in the competition.
Martin Hunter's young side reached the first knockout stage, where they were beaten 4-3 on penalties by Reading at St Mary's, having previously beaten Colchester and Crawley to win their group.
Hunter, Saints' technical director, hailed the benefit of playing in the competition.
"It has been very, very beneficial for our young players," he said.
"It’s another piece in their jigsaw, in terms of people saying that they don’t get enough of an opportunity to play against men.
"It’s the acid test, to quote an old cliché. The small stadium pitch here at Staplewood is good, but you need experience of playing at places like Charlton and St Mary’s.
"It’s been very important for their development and their learning curve."
Now, the options, which also include reverting the competition to English Football League clubs only, were spelled out by EFL chief executive Shaun Harvey at a meeting of the 48 clubs on Tuesday, with his preference clearly being a continuation of this season's 64-team competition involving 16 category one academy sides.
The new format has dramatically divided opinions within the game, as many fans have boycotted the matches because of fears this is a Trojan horse to introduce Premier League B teams into the league pyramid - an idea suggested by former Football Association chairman Greg Dyke in 2014.
Harvey, however, has denied this and did so again at the meeting at Walsall's Banks's Stadium, where he suggested relaxing the rules on the number of changes the EFL sides can make to their teams, keeping the competition regional until the quarter-final stage and adding more money to the prize fund.
In a press release, Harvey said: "We committed at the outset of this season's competition to conduct a full and comprehensive review of the competition and, importantly, give our clubs the ability to ensure they make the key decisions regarding where we take the competition in 2017/18 and beyond.
"After asking clubs in advance for some initial thoughts on the competition, today was the next stage of the process and I'm delighted we were able to have such a full and frank exchange of views that will now assist the executive in refining a final proposal that our clubs will now vote on."
Formerly known as the Johnstone's Paint Trophy, the competition was overhauled this season in an attempt to reverse waning interest from clubs and fans.
The idea was to combine the desire of the Football Association and Premier League for more first-team opportunities for young English talent, with the competition's traditional appeal of a Wembley final for League One and Two clubs.
Harvey had hoped all the Premier League clubs with the top-ranked academies would accept the invitation to field largely under-21 teams in the competition but six of those invited chose not to take part, which meant seven Championship sides entered their academies.
This disappointing start to the competition continued in the group stages, where many clubs broke new records for low attendances And the negative publicity the competition received was not helped by the fact many EFL clubs tried to get around the "full-strength" rules they had to comply with, a situation that led to 12 clubs being fined for fielding weakened teams and others substituting senior players after only a few minutes of the game.
Having asked the clubs for feedback, Harvey has suggested relaxing the full-strength rule so EFL clubs only have to play four first-team outfield players and broadening the definition of a first-team player to include anyone on loan from a club with a category one academy or who has played 40 games. If these criteria were applied this season, only two fines would have been levied.
This season's competition was regional in the group stages and then an open draw for the first knock-out round of 32. Harvey is proposing to keep the rounds of 32 and 16 regional next season, as well as giving clubs the flexibility to schedule games outside of international weeks - a tweak that could see more Premier League sides join in.
But perhaps the most compelling argument presented for continuing with the experiment is the promise of more prize money. This year the Premier League put another £1million in the pot and it is understood that could stretch to £2million next season.
Coventry City beat Oxford United earlier this month in the first Checkatrade Trophy final, in front of a crowd of more than 70,000 fans - a positive end to what had been a difficult campaign. But Harvey has been adamant the competition met its targets for developing players and increasing revenues.
The EFL clubs shared three-quarters of the almost £2million prize fund, three times what they earned last season, while 27 per cent of players in the starting line-ups this season were under-21 and English, compared to 23 per cent in 2015-16 and 18 per cent in 2014-15.
The EFL board will now refine those proposed changes to the format before putting the three options to the clubs again at the annual general meeting in May.