The Whites defender met his new boss for the first time last week.
Leeds' Liam Cooper (R) and Charlie Taylor applaud the away fans
Cooper, who admits he felt "buzzing" after hearing of Monk's appointment at the start of the month, caught up with the 37-year-old briefly at the Whites' Thorp Arch training ground last week.
"He (Monk) was a centre-half and he likes to play football, so I think I’m going to learn a lot from the manager," the 24-year-old told LeedsUnited.com.
"I can’t wait to get going and start building relationships with the staff.
"He told me he’s buzzing to get going with the young players. He wants to forward our careers, like we all do – we all want to play in the Premier League."
However, the excitement doesn't end with Cooper, who added: "From speaking to a few of the boys, they can’t wait to get started as well."
With a squad of more than 20 players already, Monk is likely to rely primarily on those already at his disposal, barring any sales.
In demand? Leeds midfielder Lewis Cook
A large number of those are graduates of the Whites' academy, though with three out of contract in 12 months' time it is feared they could be sold on before their values decrease even further.
Lewis Cook and Charlie Taylor have already been linked with moves to Premier League clubs, with Everton said to be keen on the former (Sun), and city rivals Liverpool listed as potential Taylor suitors (Teamtalk).
Alex Mowatt is the other Thorp Arch product whose deal expires next summer, with Cooper and defensive partner Sol Bamba among the non academy graduates out of contract.