Willock scored a stunning eight goals in 14 Premier League appearances after joining Newcastle on loan in February and was instrumental in steering them well clear of the relegation zone to finish 12th.
"Of course we want him back, he did great with us and gives us another dimension in midfield that we haven't got," Bruce said after his side beat Doncaster Rovers 3-2 in a friendly on Friday.
"We'll keep bashing away at it."
But Bruce wants a firm answer.
"With Arsenal, what are they going to do?" he added.
"They've brought in two midfield players. That's our starting point, with Joe, because let's be fair, he had an unbelievable three or four months with us. But there has to be a time where we know – is it going to be yes or no?
"We're only allowed two domestic loans, and we're only allowed one from each club. So, there has to come a time when there's a cut-off, and we have to find out what's happening. We're still trying our utmost, whether it's on loan or to buy him. We're still trying."
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