The 21-year-old was on loan with the Magpies last season and quickly became a key player, scoring in each of the club’s last seven games.
His goals were crucial as Newcastle pulled away from trouble and eventually finished safely in 12th place.
Bruce is understandably keen to bring attacking midfielder Willock back to Tyneside but admits that Arsenal hold all of the cards.
He said: “As I’ve said, it’s really Arsenal’s decision, and until Arsenal make a decision – a bit like all the big clubs, they have a look over pre-season – we’ll keep monitoring and badgering away.
“We’d love to do something but it’s still Arsenal’s call.”
Arsenal manager Mikel Arteta said last week that Willock “is part of our plans” but is looking to reshape his midfield with Granit Xhaka expected to leave.