Chris Wilder has previously joked about the extent of his European ambitions being an end-of-season trip to Magaluf. He has tempered that by saying he will have a look at adjusting pre-season when it looks like qualification is possible.
For those who have flown high in the Premier League before, it looks very realistic. There are parallels with Norwich City, in 1992-93, and Ipswich Town, in 2000-01, who qualified for the UEFA Cup and made golden memories against the biggest clubs in the world.
Then came the reality check, back to the battle of domestic football and in both cases a fight against relegation not far around the corner. Burnley, in 2018-19, were the most recent club to feel the effects of a shock rise to rub shoulders with the heavyweights.
Bryan Gunn, Norwich goalkeeper for their magical journey which included Bayern Munich, sees similarities between his team and Wilder's Sheffield United, not least their underdog status.
"We were a team that people admired, but we were taken as the country bumpkins when we drew Bayern and there was a little bit of a lack of respect - not disrespect - which helped us," Gunn said. "We got the message and the experienced players wound each other up. The manager was good at that as well.
"We had John Deehan, who was a very technical coach, so a lot of our play was based on a European game and like Chris Wilder's system now with overlapping centre-backs. It's very difficult to play against."
Norwich's third-placed finish in the inaugural Premier League had similarities to Sheffield United. While they had secured high-placed finishes in the 1980s, the previous campaign they were 18th.
The UEFA Cup campaign is the stuff of legend in Norfolk, beating Bayern in the second round when Jeremy Goss' stunning volley was among the goals, then losing to an Inter Milan team inspired by Dennis Bergkamp.
"It is something to look forward to for lads who haven't experienced it before," Gunn said. "Even lads at Sheffield United who haven't been involved in internationals, there is talk of them being called up. It shows you success breeds success and reward."
From such incredible highs came the low of the following season when Norwich were relegated. Gunn says it was bad luck with injuries and not having cover, which Sheffield United addressed in the January window by bringing in Sander Berge, Panagiotis Retsos and Richairo Zivkovic to compete for first-team places.
"We were unlucky," Gunn said. "On December 28 that season I got stretchered off with a broken leg. It's about strengthening and having players in the right positions at the right times.
"It can easily catch up with you if you don't keep your eye on it. Sheffield United have the ability to strengthen their squad and have probably done it now in a way that they don't need to do much in the summer."
Norwich's rivals, Ipswich, shocked the Premier League when they finished fifth in 2001 and qualified for Europe. By then the UEFA Cup had moved to the Thursday and George Burley, their manager, believes European football played a part in them getting relegated that campaign.
They had beaten an Inter Milan team including Clarence Seedorf and Javier Zanetti in the first leg of their third-round tie, then a few months later were facing the prospect of life in the second tier.
"It had a big impact," Burley said. "When you are in the Premier League every game is so tough to pick up points, so your concentration level has to be focused. Then you introduce another match on the Thursday. If you have 12 to 14 international players your squad can cope with it, but if you haven't it is very difficult. We were relegated the next season, finishing third bottom.
"I'm convinced that if we hadn't been in Europe we would have stayed up. But you're not going to say: 'I don't want to be in Europe.' It comes with success, but it's just very difficult for a small club to compete with clubs that have been in Europe year after year.
"They are great memories and you don't look back and think you should have done it differently. I still live in Ipswich and the memories of the fans I speak to are happy ones."
Sean Dyche thought the Europa League was a distraction for Burnley last season, suggesting "all the outside noise" about the competition took the edge off his team's performances in the Premier League. They did not win a game until they were knocked out of Europe, in late September, and ended the season 15th but with just 40 points.
Wilder's recruitment suggests they are ready. Another question would be whether Europe is ready for Sheffield United? Pre-season plans have been put in place.
Wilder got the best out of players with a trip to Portugal last summer, but plans could change if they continue their good form.
"It would only be right that we did that, but only when we get into the position where it might be a possibility," Wilder said. "We're 13 games off until the end of the season and there are a load of points to be won and lost, so I'm always realistic and I never get ahead of myself.
"We live in the present. I've already planned our pre-season. It is a really important period. We'd love to be in a position to adjust it, but we will only talk about it when the position gets closer."