Murphy is understood to be keen on making the move and a second bid from Newcastle would encourage the 22-year-old, who played for the Under-21 squad that reached the semi-finals of the European Championships in Poland last month, to push to leave Carrow Road. "We have to try to do our best", Benitez said.
Benitez was told to expect up to £100m to spend on new players following "positive" discussions with the owner.
A year ago Rafa Benitez made clear that he was building a team that was specifically structured to get the club out of the Championship at the first attempt, with then further major work being needed to be done if they were then indeed promoted.
And Benitez claimed he is not giving up hope on bringing more players through the door, but will ensure they are right for the squad.
"We know where we are - that is not ideal because everybody wants to see a lot of players signing already - but we have to keep working and see what we can do".
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Speaking at the club's 1892 Foundation Cup event, Benitez continued: "We can do nothing other than just keep working to find the players that we want, and hopefully we can do it".
"We can do nothing else".
But, speaking at the club's 1892 Foundation Cup event, Benitez said: "It's not easy for a lot of teams because the market is a little bit insane".
"Obviously, the top sides have a lot of money. The other teams are spending too, but we will see what we can do".
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