Sparrow has not played at all in United's pre-season campaign, but has stepped up his training in the past week.
And after doing well in a training match on Tuesday, Sparrow has every chance of featuring on Saturday.
"He ran around in the game as if he had done a full pre-season," Adkins told BBC Radio Humberside.
"He trained well last week and on Monday, we'll assess him on Thursday.
"Sparrow is a Championship-quality player. He's an integral player, but if he's not quite right then I'm not going to risk it."