Ole Gunnar Solskjaer is keen to add attacking reinforcements to his squad before the deadline, with Donny van de Beek still the only arrival in the current window despite links to a number of high-profile players.
Borussia Dortmund winger Jadon Sancho remains United's top target, although differences in the valuation of the England international have seen those talks stall.
The Manchester Evening News reports that Brooks was never considered as an alternative for Sancho, and that the Red Devils have ended their interest in the midfielder for now.
United have also parked their centre-forward pursuit to rule out a return for academy product King, although they could revive their interest in him in January when Odion Ighalo's loan spell ends.
United would have until October 16 to complete a deal for the Bournemouth duo, with next Monday's deadline only applying to international transfers and deals between Premier League clubs.