Swansea City striker Oli McBurnie

The Scottish international will now undergo a medical at Bramall Lane ahead of a club-record move to South Yorkshire. United returned to south Wales with an improved bid, after their first offer of £15m was rejected by officials at the Liberty Stadium.

United are thought to be paying in the region of £17m for McBurnie, which could rise as high as £20m with add-ons.

Barring any unexpected hiccups McBurnie, who scored 22 goals for the Swans in the Championship last season, will become United’s new record signing – the fourth time this summer they have broken their highest fee. Luke Freeman, Callum Robinson, Lys Mousset and now McBurnie all broke the record this summer.

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United have also signed Dean Henderson, Ravel Morrison, Phil Jagielka and Ben Osborn since they won promotion to the Premier League.

McBurnie has been a long-time target of Blades boss Chris Wilder, who was interested in signing him when United first came into the Championship. But Swansea, recently relegated from the Premier League, instead offered him a new contract.