Winger Johnson missed Tuesday night's 3-1 FA Cup fourth-round replay win at Fulham after undergoing minor thumb surgery, while midfielder Rodwell (knock) and forward Wickham (calf) also sat out the Craven Cottage clash.
Poyet refused to rule out any chance of the trio being involved on the return to top-flight action at the Liberty Stadium but bemoaned the number of his squad that have joined Lee Cattermole (knee) on the sidelines over the past week.
"It will be touch and go for Adam Johnson so it is a big decision, but we have got a few of them," Poyet told his club's official website.
"It is incredible that on Wednesday last week we had 20 players available with Lee Cattermole the only one out, and then we went from there to having five or six out of Saturday.
"There are a few decisions to make tomorrow. I think one [Rodwell or Wickham] of them has a chance but the other one doesn't, but we will wait until Friday."
Emanuele Giaccherini and Ricky Alvarez reminded their boss that he has plenty of attacking options in midweek despite any injury dilemmas.
Both impressed and Alvarez scored his first goal for the club as Sunderland overhauled Hugo Rodallega's opener.
"You need to be smart in your squad and it is important to have options so you can adapt to different games," Poyet said.
"The mobility of Giaccherini and the ability of Ricky helped us a lot in the game against Fulham and if they can bring that week in week out it is going to be difficult for the rest to get back in the team.
"I always say to the players to be in the team when it clicks and we start winning because then it is going to be difficult to take you out."
Sunderland ended a five-match winless run in the Premier League when they beat fellow strugglers Burnley on Wearside last weekend - Wickham and January recruit Jermain Defoe getting the goals.
Swansea were winless in four league outings and had suffered an FA Cup exit at the hands of Championship outfit Blackburn Rovers before they got back on track with a 1-0 win at high-flying Southampton, courtesy of Jonjo Shelvey's spectacular 83rd-minute strike.
Manager Garry Monk celebrated one year in charge at the Liberty this week and he is boosted by having defender Kyle Bartley and midfielder Ki Sung-yueng available against Sunderland.
Bartley was sent off at Blackburn, while Ki was part of the South Korea squad that reached last weekend's Asian Cup final.
Gylfi Sigurdsson serves the second game of a three-match ban following his own red card in the Rovers reverse.
