Jetta has missed the past 10 matches with a troubling shin problem, while Reid has played just 10 minutes of football over the past 11 games due to a recurring quad issue.
Both are due to take part in full training on Saturday - a positive sign for their hopes of playing a part in the club's premiership defence starting next month.
The Swans' reserves have a bye this week before commencing their NEAFL finals campaign, so they've agreed to take part in a full training session, when they will be joined by Jetta and Reid.
"It's a bit of a four-horse race with those four," Swans physio Matt Cameron told the club's website of the injured quartet, which also includes Lewis Roberts-Thomson.
“We’ve probably got Reid and Jetta out in front and Jetta is definitely going to be training with the team on the weekend in the twos.
“The reserves don’t have a game this weekend, so they’ve all put their hand up to train on the weekend with Lewis.
“Sam should train as well.”
Swans players typically need to get through at least a full week of solid, uninterrupted training prior to being selected in the team the following week.
That means Goodes is now unlikely to feature before the finals series gets underway.
The Swans, who have secured a place in the top four, face the Cats in Geelong on Saturday and Hawthorn at ANZ Stadium the following week before their finals campaign commences.
Goodes, Jetta and Reid were all considered to be around the same level in their recovery and a little ahead of Roberts-Thomson (knee), who has been sidelined since round four.
But Goodes is now in a similar race to Roberts-Thomson and won't return to training until next week at the earliest.
That would mean week one of the finals would be the earliest the dual Brownlow medallist could be expected to return to the side.
"Adam and 'LRT' are running at the moment and are increasing their speed and are working on their agility,” Cameron said.
“We’re hoping to have them join the training with the team next week.”
Across town, Greater Western Sydney has started preparing for next season by putting a number of players under the knife.
Devon Smith's season is over after he underwent hip surgery as the club aims to get him 100 per cent fit ahead of pre-season training.
Smith played 18 matches this season to take his GWS tally to 38, third on the club's all-time list behind Jonathan Giles and Callan Ward, who have both made 40 appearances.
Teammates Aidan Corr (ankle), Will Hoskin-Elliott (hip), Sam Reid (hip), Rhys Palmer (foot), Jacob Townsend (hip) and Andrew Phillips (hip) have all had surgery in recent weeks and are focusing on 2014.
First-year Giant Jono O'Rourke faces a test on his injured shoulder to determine if he is fit to return for the reserves' opening NEAFL finals match this Saturday.
