The Spaniard missed the draws with Chelsea and Southampton after picking up a dead leg in the Capital One Cup victory over Liverpool at Anfield.
Flores may have to wait to reclaim his place in Michael Laudrup's starting line-up with club captain Garry Monk impressing alongside Ashley Williams in the centre of the Swans' defence, but hopes to return to training on Thursday ahead of the visit to Tyneside.
"I'm still feeling a bit of pain, but it has improved a lot," he told the club's official website.
"I am hoping to return to full training on Thursday to see how it reacts.
"Like all players, I want to play week-in, week-out, and I am not the type of person who likes to leave the field with an injury. But I just couldn't carry on at Liverpool; it was too bad. I thought I would recover after three or four days, but it just got worse and has dragged on.
"It was particularly disappointing because I thought I was at a good level after coming back from suspension. I was feeling comfortable on the pitch and with the team.
"My English is improving all the time, and although it's still early days, I understand my team-mates a lot more and can express myself better.
"The injury is a blow, but I hope to be fit and performing well again soon, hopefully at Newcastle on Saturday."