Absent since limping out of the home defeat to Cardiff on December 22 with a heel injury, Vardy got 45 minutes under his belt in a behind-closed-doors friendly this week and has now resumed full training.
The striker's fitness is being monitored to see if he is fit enough to be involved at Ashton Gate.
"Jamie played part in a game that we had here (at the training ground) the other day, came through it ok and will be training with us today (Thursday)," Pearson said.
"We'll have to see how it goes. I'm not ruling him out, but we'll see how he is."
Vardy is not the only one making progress from the treatment room, with defenders Sean St. Ledger (hamstring) and Zak Whitbread (calf) and midfielder Richie Wellens all taking steps towards a return to full fitness.
"St. Ledger is making some progress and Zak should be available before too long," said Pearson. "Richie Wellens is on his way back too so, for the most part we're not too bad."
Leading scorer David Nugent could return to the starting line up after the 12-goal striker began on the bench against Burton last weekend in the FA Cup.
French winger Anthony Knockaert, also a substitute for the third-round tie, is another player with a strong case for a recall.