Excitement is buzzing around the Swede, but Pardew is unconvinced.
After defeat at Liverpool, Pardew told talkSPORT: "Can I tell you what I'd be concerned about if I was an Arsenal fan? Gyokeres, so far.
"I'm looking at him and thinking, 'I want a bit more from you!' Sporting is different because it's a different kind of culture and Sporting was a great team that he was in and he was always going to get goals there.
"But when he was at Coventry, he looked looked quick down the side of the pitch, proper quick. Now, in the Premier League, he didn't look quick today did he?
"There was times when he had the march and didn't get past the centre-backs. It's a concern whether this kid can step up and be this number nine that Arsenal have been waiting on for three years.
"There is a lot of pressure on him and I really hope he does crack it, but I thought today he was quiet."