The Blades head to Chelsea on Saturday looking to build on a solid start to life in the Premier League.
After an away draw at Bournemouth, Chris Wilder’s side beat Crystal Palace at Bramall Lane, before slipping to defeat to Leicester City.
Leeds-born McBurnie was a used substitute in all three games - netting against the Foxes at Bramall Lane after coming off the bench - and started for United in the midweek League Cup win over Blackburn Rovers.
The 23-year-old former Barnsley and Bradford City forward was replaced at half-time, with Wilder having one eye on Saturday.
“He has been pushing (for a start) and he has scored,” said Wilder. “I am obviously not going to sit here and tell you my team, but he is well in the forefront of our plans going into Saturday.
“We brought him here to play, it took a bit of time to get into the team, but he’s made contributions off the bench against Bournemouth, Palace and Leicester.
“He’s knocking on the door to play.”
Wilder made 10 changes for the Cup game, and admits the competition for places at the Lane is a welcome problem to have.
“These are good dilemmas to have, I want problems and issues,” he said. “I want people to be knocking on my door and be challenged, in terms of picking the side.
“You don’t want it just to be a 12-14 man group, it has to be 20-22, and even more really, because of the intensity and competitive aspect of the Premier League.”