Sheffield United have agreed a £17m deal, rising to £20m, with Swansea for striker Oli McBurnie, according to Sky Sports News.
McBurnie began a medical at Sheffield United on Wednesday night and will continue undergoing tests on Thursday.
The move will break the newly promoted Premier League side's transfer record for a fourth time this window.
The 23-year-old scored 22 goals and made four assists in 42 Sky Bet Championship appearances last term.
McBurnie helped Swansea to a 10th-place finish in 2018/19, and has two years remaining on his current deal at the Liberty Stadium with the option for a further season.
The Scot would become Sheffield United's eighth signing of the summer transfer window.
Dean Henderson recently arrived at Bramall Lane on a second successive season-long loan from Manchester United, while Ben Osborn has also joined the Blades for an undisclosed fee from Nottingham Forest.
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