The former Bristol City manager was forced to field a make-shift back four in the 3-2 defeat to Bury last weekend with Jamie McAllister (ankle), Byron Webster (hamstring) and Dan Burn (ankle) all missing out at Gigg Lane.
And Johnson says he will give his walking wounded until Friday to declare their fitness for one of the biggest matches in the club's history.
Matt Dolan and Nathan Ralph are also doubtful with knee injuries but Reuben Reid could be included on the bench having returned from his loan spell at Plymouth.
The Glovers ran out 2-0 winners at Bramall Lane in the League One meeting between the sides back in January and midfielder Ed Upson says the Glovers can take heart from that result.
"We played well there this season so that is a big positive for us and it would be great if we could recreate that," he told Press Association Sport.
"Obviously it will be a different game but if we can get anywhere near that level we'll be doing alright."
Gary Johnson's squad left Huish Park for St George's Park, the new FA Football Centre at Burton, on Thursday morning.
The Glovers will be based there for three days with hydro-pool therapy planned on Saturday morning in preparation for Monday's second leg.