Manchester United striker Rooney has been linked with Arsenal during the summer, along with fellow forward Gonzalo Higuain and Everton midfielder Marouane Fellaini.
But Wilshere believes the signing of his fellow England international from the Premier League champions would provide the biggest impact.
"If it happens, it would be amazing," he told ESPNFC.
"He is the type of player who can win you trophies - and just to see his name on the team sheet brings fear to the opposition. We could do with a little more of that.
"You look at the type of players like Higuain we are trying to bring in and you have got to be encouraged.
"I think we need a few more, not to step right into the team, but to add to the squad."
Wilshere, 21, believes adding quantity and quality to their ranks will be crucial if they are to bring silverware to Emirates Stadium.
He added: "We need our squad to be as deep as United's and (Manchester) City's. They can change their back four completely and still win. There is no way United would have won the Premier League trophy with 18 players."
Wilshere added: "It is no secret we need to win a trophy. How long has it been now, seven or eight years?
"The players feel the pressure and we have gotten close a few times like with the Carling Cup a couple of years ago.
"I think once we win one, others will follow."
Wilshere saw his own progress last season hampered by a series of niggling injuries, but feels the ankle is now "100 per cent" as he prepares for Arsenal's tour to Asia.
"I am really looking forward to having a solid pre-season. I haven't had one in two years and once you miss it, you are always playing catch-up," he said.
"It's a chance to show the manager that you deserve to be in the team and I think there's going to be competition for a few spots, but that's a good thing.
"If you're going to challenge for trophies, you need a big squad. You can't expect 11 players to do it every week."