我的意思就是买一份三个月后到期的欧洲美元期货合约==> you can't do this because the USD1 million will only be received in three months' time, doing this exposes you to interest rate risk immediately.
The answer for the question is for you to buy a "3X9 Forward Rate Agreement" (FRA)
To be more specifically, to buy a 3X9 Forward rate agreement to pay Float (floating rate) and to receive Fixed (interest rate).
To pay float because you will be receiving floating rate return from the assets and you expect the interest rate to decline after three months.
To receive fixed, because under a declining interest rate scenario, we always want to lock in the current interest rate and fixed it now.
FRA contracts are forward contracts and 3X9 FRA just means that the contract will start three months from today (to match the time where the USD1 million will be received) and ends 9 months from today (you didn't mention about the investment period for the 1 million USD to be received in 3 months time, so i assumed the investment period is 6 months just to simplify things as you mentioned 6 months LIBOR floating rate in the question).
Hope this helps!
Cheers