Head coach Vitor Matos has revealed the striker’s recovery is ahead of schedule and hopes to have the £6m frontman available before next month’s international break.
Idah’s return would provide a significant boost for the Swans as they look to maintain momentum in the Championship.
The Republic of Ireland striker is edging closer to a return following a serious hamstring problem that sidelined him just before Christmas.
The 24-year-old, who was initially ruled out for up to three months, has now stepped up his rehabilitation after returning to light grass-based training at the club’s Fairwood complex last week.
"It's always good when we have more options with different profiles," Matos said.
"So far we are really happy, like you all know, with Vipi (Zan Viptonik) and as well with different solutions where we can use either Liam [Cullen] and Mel [Widell].
"But we are really happy for Adam. He has to keep going in terms of recovery and let's hope everything goes well."
Swansea welcome Bristol City to the Swansea.com Stadium on Saturday.
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The Swans go into the fixture in strong home form, having moved 10 points clear of the relegation zone and remaining unbeaten in their past seven home games.
Matos will, however, be forced into at least one change after midfielder Marko Stamenic was handed a two-match suspension following his tenth booking of the campaign in the defeat at Derby County.
The head coach has backed Jay Fulton to step in and play a key role.
"That happens," Matos said after the game.
"Marko is a really good player, really important for us of course but Jay is as important as him, like all the players in the squad and I think the most important thing is that we, as a team, always react and always find a solution and that's what we're going to do."
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Fulton, who recently signed a two-year contract extension alongside goalkeeper Andy Fisher, is the club’s longest-serving player after joining from Falkirk in 2014 and has now made more than 300 appearances in a Swansea shirt.
"It's brilliant news. They [Fulton and Fisher] both represent a lot of what we want to build," Matos added.
"Jay has been at the club for so many years and I think he's doing unbelievable work. He's someone really important for the squad, he's someone important for the club. The level that he's playing is as well something that we all like to see.
"So I'm really happy for him, really happy for the club".
Saturday’s visitors Bristol City arrive with their own ambitions, having cut the gap to the Championship top six to just one point following a midweek draw with Wrexham.
While both sides still harbour play-off hopes, the Robins currently appear better placed as the season moves into its decisive phase.
Swansea have lost three of their last five league games against Bristol City (W1 D1), after only losing one of their previous eight beforehand (W4 D3).
But the Swans have also won six of their last seven home league games (D1), with no other Championship side collecting more home points than the Swans (19) since that run began in December (level with Ipswich Town).
