McGoldrick has missed the last four games with a groin injury that also ruled him out of the Republic of Ireland's Euro 2020 qualifiers, but the Blades hope the extra rest and treatment during the international break will have done the trick.
The same can be said for both McBurnie and Fleck as well. The former pulled out of the Scotland squad with a knee problem and has been undergoing treatment since, while Fleck made his debut for the Scots against Russia before also withdrawing through injury.
Blades boss Chris Wilder is unlikely to take any risks, but hopes some of the trio will be able to figure.
Arsenal have no fresh injury worries to concern them but hope to have striker Alexandre Lacazette back in action for the first time in a while.
The France international has been sidelined since Arsenal's 2-2 draw with north London rivals Tottenham on September 1 but has been back in full training and could play some part at Bramall Lane.
The Gunners are going well so Unai Emery is unlikely to change a winning side, but Lacazette will be hoping to take a place on the bench.
Elsewhere, teenage midfielder Emile Smith Rowe is available for selection again after recovering from concussion, but Reiss Nelson is not quite ready as he battles back to full fitness after suffering knee ligament damage.
The Blades go into the game having lost their last three Premier League games on home soil to leave them sitting in 15th place in the table, just one point above the relegation zone, but could jump to midtable with a win.
Arsenal are fifth but could jump above Chelsea and Leicester into third place with all three points.