The media outlet claims that a fee of £12m is enough to see the Yorkshire side part ways with the midfielder, with a medical now expected to take place over the next 24 hours, before confirmation of Brooks' move to the Vitality Stadium.
Brooks enjoyed a fabulous campaign in the Championship last season for the Blades, scoring three times and providing five assists in 30 league games, earning the club's Young Player of the Year award as a result.
Despite signing a new four-year deal in October however, Brooks now looks set to be Eddie Howe's first summer signing for the Premier League side, who are looking to kick on in what will be their fourth season in England's top division.
An exciting prospect, Brooks is an adept attacker able to play anywhere across the forward line, although his preferred position under Chris Wilder at Bramall Lane was as an attacking midfielder, able to drift into dangerous positions in the final third.
The 20-year-old boasts international experience also, winning three caps for Wales after making his debut in November after switching allegiances from England. He had previously played for the Three Lions in the younger age groups, even scoring in the 2017 Toulon Final.
News of Brooks expected arrival comes in the wake of a forward leaving the Cherries, as Max Gradel recently ended his time on the South Coast and returned to Ligue 1, joining Toulouse permanently after spending last season on loan with the French side.