Burke missed Tuesday's home match with Colchester United after twisting his ankle late on in the previous match at Blackpool. Thomas suffered a tight groin during the Colchester game in midweek and had to be taken off early.
Free from injury now though, Thomas is expected to come under consideration for one of City's striking berths at Gigg Lane.
Parkinson admits, however, that he is unsure at the moment whether to bring Burke straight back into the team or to save him for next Tuesday's rearranged home game against league leaders Burton Albion.
The City chief said: "Wes is fine and he is available for Saturday.
"Reece has been training with the rest of the squad today (Friday) but we will just make a call on him ahead of the game to decide whether we bring him back into the side or hold him back for the Burton match."
Steven Davies won't be in City's plans for the Bury match as he prepares for a spell on the sidelines but Parkinson has revealed that the striker's injury isn't as bad as first feared.
Parkinson added: "The news on Steven is a lot more positive.
"He had a scan on the injury at the start of the week and it showed that the cruciate ligament is intact.
"The specialist is happy with the situation regarding his knee as well. It is just a case of him going through his rehab and hopefully getting him back sooner rather than later.
"Steven has damaged his knee badly earlier in his career so when the swelling came up after jarring it at Blackpool, it was only natural from him to think the worst.
"That swelling has gone down now which is great news for us and great news for Steven.
"We don't know exactly when he will be back but it is certainly better than we first thought."