Willock has been on loan at Newcastle since January after joining until the end of the current season.
The 21-year-old has impressed, with his goal in the win over Leicester last Friday his fourth in as many games.
And Bruce confirmed on Monday morning that Newcastle would like to keep hold of the midfielder on a permanent basis this summer.
“All of us would love to [make it permanent],” Bruce told talkSPORT.
“He’s 21, a midfield player and he’s got five goals since the turn of the year, so of course we want him – but we have to respect that he’s Arsenal’s player.
“I’m sure Arsenal will have big discussions this summer, but if there’s a possibility that we can bring him back we’d love to do it.”
Willock will have two years left on his contract at Arsenal come the summer and it has previously been reported that Newcastle believe they can land him for around £20million.