Jesus claimed his first Gunners goals since his summer switch from Manchester City by netting twice in last weekend’s 4-2 Premier League success over Leicester.
Parker, whose newly-promoted Cherries are bidding to bounce back from a 4-0 thrashing at champions City, is full of admiration for the Brazil international and braced for another severe test when Mikel Arteta’s men visit Vitality Stadium on Saturday evening.
“Gabriel Jesus is a brilliant signing, an amazing signing really,” said Parker. “Mikel had the player at Manchester City and he’s a top forward, an incredible centre forward.
“He’s probably got every facet to his game as a number nine: can drop in, can link play, is also a threat on your backline as well, endless work-rate in terms of pressing and leading the line from that sense.
“It’s a real challenge for us at the weekend to try and keep him quiet, he’s a big player for them.”
Arsenal are one of only two clubs with a 100 per cent record following the opening two rounds of top-flight fixtures, alongside Pep Guardiola’s early leaders.
The north London club were bottom of the division after losing their opening three matches last season.
Having ultimately missed out on Champions League qualification to rivals Tottenham last term, Parker has backed the Gunners – who also recruited Oleksandr Zinchenko this summer – to be “right up there this year”.
“What Mikel has done in a short space of time is fantastic,” said Parker. “The progression they’ve made in terms of signings has enhanced them even more.
“I seriously see them as a team that are going to be right up there this year. They’re a technical team with huge quality all over the pitch.
“We’ll embrace that, we’re ready for that and we’ll do the work we can to try and nullify that and try and make it uncomfortable as much as we can, while also understanding the challenges that we’re going to face and the problems they’re going to cause.
“We have a big challenge ahead of us.”