Tuesday night’s 2-0 home win over Port Vale, which came after extra-time, sent the Iron further in the competition than they have been before.
The draw for the next round takes place at dinnertime on Saturday – when United will be taking on Doncaster Rovers at Glanford Park in a match that is being played early at the request of Humberside Police.
"At one minute past 12 on Saturday when the fourth-round draw is made, we will be one nil up and there will be a big cheer around the ground when we get Liverpool away,” joked Adkins, who was born in Birkenhead on the Wirral so grew up in the shadow of the Reds.
“That would be nice wouldn't it.”
It certainly would, although there is no guarantee of a Premier League tie for the Iron: Peterborough United and Barnsley also reached the last 16 on Tuesday.
Cardiff City, Preston North End and Queens Park Rangers will also be in action on Wednesday night trying to join them.
This is the first time the Iron have reached this stage of the competition and Adkins said the win was fully deserved.
"It was an excellent performance and an excellent result, I thought we played some great football and entertained the supporters,” he said.
"We even gave the supporters half an hour of extra entertainment. We had 41 attempts at goal and I thought we gave them something to enjoy."
Micky Adams, the Port Vale manager, felt his side could travel back to Stoke with pride from their cup run.
"We can be proud of what we have done, with a bit of luck, it might have gone our way," he said.
"We had chances in the first half and we had chances in extra time after they scored. Their keeper played really well in extra time. It just wasn't our night."